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Stigler Diyet Sorunu

Bu bölümde, adını ekonomi alanında Nobel ödüllü George Stigler'dan alan ve bir dizi gıdanın temel besin ihtiyaçlarını karşılamanın pahalı olmayan bir yolunu hesaplayan Stigler diyeti adlı klasik problemin nasıl çözüleceğini göstereceğiz. İdeal beslenmeyi hesaplama fikri son zamanlarda popüler hale gelmiş olsa da, bunu yemek önerileri olarak değil, matematiksel bir alıştırma olarak ortaya koydu.

Stigler diyeti şu minimum değerlerin karşılanmasını zorunlu kıldı:

Besin listesi

Besin Maddesi	Günlük Önerilen Alma
Kalori	3.000 kalori
Protein	70 gram
Kalsiyum	0,8 gram
Demir	12 miligram
A vitamini	5.000 IU
Tiamin (B1 Vitamini)	1,8 miligram
Riboflavin (B2 vitamini)	2,7 miligram
Niasin	18 miligram
Askorbik Asit (C Vitamini)	75 miligram

Stigler'ın değerlendirdiği yiyecek seti zamanın (1944) bir yansımasıydı. Aşağıdaki besin verileri birim başına değil, dolar başınadır. Bu nedenle amaç, her bir gıda maddesine ne kadar para harcanacağını belirlemektir.

Ürün listesi

Emtia	Birim	1939 fiyatı (sent)	Kalori (kcal)	Protein (g)	Kalsiyum (g)	Demir (mg)	A vitamini (KIU)	Tiamin (mg)	Riboflavin (mg)	Niasin (mg)	Askorbik Asit (mg)
Buğday Unları (Zenginleştirilmiş)	10 lb.	36	44,7	1411	2	365	0	55.4	33.3	441	0
Hardal	1 kg	14.1	11.6	418	0.7	54	0	3.2	1.9	68	0
Buğday Gevreği (Zenginleştirilmiş)	28 oz.	24.2	11.8	377	14.4	175	0	14.4	8.8	114	0
Mısır Ezmeleri	8 oz	7.1	11.4	252	0,1	56	0	13.5	2.3	68	0
Mısır Unları	1 kg	4.6	36.0	897	1.7	99	30.9	17.4	7,9	106	0
Hominy Gritleri	24 oz.	8.5	28.6	680	0,8	80	0	10.6	1.6	110	0
Pirinç	1 kg	7.5	21.2	460	0.6	41	0	2	4.8	60	0
Yulaf Ezmeleri	1 kg	7.1	25,3	907	5.1	341	0	37.1	8.9	64	0
Beyaz Ekmek (Zengin)	1 kg	7,9	15.0	488	2.5	115	0	13.8	8.5	126	0
Tam Buğdaylı Ekmek	1 kg	9.1	12.2	484	2.7	125	0	13.9	6.4	160	0
Çavdar Ekmeği	1 kg	9.1	12,4	439	1.1	82	0	9.9	3	66	0
Pound Pasta	1 kg	24,8	8.0	130	0.4	31	18,9	2.8	3	17	0
Gazlı Krakerler	1 kg	15.1	12.5	288	0.5	50	0	0	0	0	0
süt	1 qt.	11	6.1	310	10.5	18	16.8	4	16	7	177
Buharlaştırılmış Süt	14,5 oz.	6.7	8.4	422	15.1	9	26	3	23.5	11	60
Tereyağı	1 kg	30.8	10.8	9	0.2	3	44.2	0	0.2	2	0
Oeomargarin	1 kg	16.1	20,6	17	0.6	6	55.8	0.2	0	0	0
yumurtalar	1 doz.	32.6	2.9	238	1.0	52	18,6	2.8	6.5	1	0
Peynir (Çedar)	1 kg	24.2	7.4	448	16.4	19	28.1	0,8	10.3	4	0
Krema	1/2 nk.	14.1	3.5	49	1.7	3	16,9	0.6	2.5	0	17
Fıstık Ezmesi	1 kg	%	15.7	661	1.0	48	0	9.6	8.1	471	0
Mayonez	1/2 nk.	16.7	8.6	18	0.2	8	2.7	0.4	0.5	0	0
Crisco	1 kg	20.3	%	0	0	0	0	0	0	0	0
Domuz Yağı	1 kg	9.8	41.7	0	0	0	0.2	0	0.5	5	0
Sirloin Biftek	1 kg	39.6	2.9	166	0,1	34	0.2	2.1	2.9	69	0
Yuvarlak Biftek	1 kg	36.4	2.2	214	0,1	32	0.4	2.5	2.4	87	0
Kaburga	1 kg	29.2	3.4	213	0,1	33	0	0	2	0	0
Chucka Sosları	1 kg	22,6	3.6	309	0.2	46	0.4	1	4	120	0
Tabak	1 kg	14.6	8.5	404	0.2	62	0	0,9	0	0	0
Karaciğer (Sığır Eti)	1 kg	26.8	2.2	333	0.2	139	169.2	6.4	50,8	316	525
Kuzu Eti	1 kg	27.6	3.1	245	0,1	20	0	2.8	3,9	86	0
Kuzu Eti (Kaburga)	1 kg	36,6	3.3	140	0,1	15	0	1.7	2.7	54	0
Domuz Pirzolaları	1 kg	30,7	3.5	196	0.2	30	0	17.4	2.7	60	0
Domuz Filetoları	1 kg	24.2	4.4	249	0.3	37	0	18.2	3.6	79	0
domuz pastırması	1 kg	25,6	10.4	152	0.2	23	0	1.8	1.8	71	0
Jambon, füme	1 kg	27.4	6.7	212	0.2	31	0	9.9	3.3	50	0
Tuzlu Domuz Eti	1 kg	16	18,8	164	0,1	26	0	1.4	1.8	0	0
Tavuk Kızartma	1 kg	30.3	1.8	184	0,1	30	0,1	0,9	1.8	68	46
Dana Pirzolaları	1 kg	42.3	1.7	156	0,1	24	0	1.4	2.4	57	0
Somon, Pembe (konaklama)	16 oz.	13	5.8	705	6.8	45	3.5	1	4.9	209	0
Elmayla armut	1 kg	4.4	5.8	27	0.5	36	7.3	3.6	2.7	5	544
Muz	1 kg	6.1	4.9	60	0.4	30	17.4	2.5	3.5	28	498
Limonlar	1 doz.	26	1.0	21	0.5	14	0	0.5	0	4	952
portakallar	1 doz.	30.9	2.2	40	1.1	18	11.1	3.6	1.3	10	1998
Taze Fasulyeler	1 kg	7.1	2.4	138	3.7	80	69	4.3	5.8	37	862
Lahana	1 kg	3.7	2.6	125	4.0	36	7.2	9	4.5	26	5369
Havuçlar	1 grup	4.7	2.7	73	2.8	43	188.5	6.1	4.3	89	608
Kereviz	1 tehdit	7.3	0,9	51	3.0	23	0,9	1.4	1.4	9	313
Sor	1 kafa	8.2	0.4	27	1.1	22	112.4	1.8	3.4	11	449
Soğanlar	1 kg	3.6	5.8	166	3,8	59	16.6	4.7	5.9	21	1184
Patatesler	15 lb.	34	14.3	336	1.8	118	6.7	29.4	7.1	198	2522
Ispanak	1 kg	8.1	1.1	106	0	138	918,4	5.7	13.8	33	2755
Tatlı Patatesler	1 kg	5.1	9.6	138	2.7	54	290.7	8.4	5.4	83	1912
şeftali (konaklama)	No. 2 1/2	16.8	3.7	20	0.4	10	21.5	0.5	1	31	196
Armut (konser)	No. 2 1/2	20.4	3.0	8	0.3	8	0,8	0,8	0,8	5	81
Ananas (teneke kutu)	No. 2 1/2	21.3	2.4	16	0.4	8	2	2.8	0,8	7	399
Kuşkonmaz (konaklama)	2. Sayı	27,7	0.4	33	0.3	12	16.3	1.4	2.1	17	272
Yeşil Fasulye (konaklama)	2. Sayı	10	1.0	54	2	65	53.9	1.6	4.3	32	431
Domuz Eti ve Fasulye (Konserve Fasulyesi)	16 oz.	7.1	7.5	364	4	134	3.5	8.3	7.7	56	0
Mısır (teneke kutu)	2. Sayı	10.4	5.2	136	0.2	16	12	1.6	2.7	42	218
Bezelye	2. Sayı	13.8	2.3	136	0.6	45	34.9	4.9	2.5	37	370
Domatesler (konser)	2. Sayı	8.6	1.3	63	0.7	38	53.2	3.4	2.5	36	1253
Domates Çorbası (konaklamalı)	10 1/2 oz.	7.6	1.6	71	0.6	43	57.9	3.5	2.4	67	862
Şeftali, Kurutulmuş	1 kg	15.7	8.5	87	1.7	173	86.8	1.2	4.3	55	57
Kuru Erikler	1 kg	9	12,8	99	2.5	154	85.7	3,9	4.3	65	257
Kuru Üzüm, Kurutulmuş	15 oz.	9.4	13.5	104	2.5	136	4.5	6.3	1.4	24	136
Bezelye, Kurutulmuş	1 kg	7,9	20.0	1367	4.2	345	2.9	28.7	18.4	162	0
Lima Fasulyesi, Kurutulmuş	1 kg	8.9	17.4	1055	3.7	459	5.1	26.9	38.2	93	0
Lacivert Fasulye, Kurutulmuş	1 kg	5.9	26.9	1691	11.4	792	0	38.4	24,6	217	0
kahve	1 kg	22,4	0	0	0	0	0	4	5.1	50	0
Çay	1/4 lb.	17.4	0	0	0	0	0	0	2.3	42	0
Kakao	8 oz	8.6	8.7	237	3	72	0	2	11.9	40	0
Çikolata	8 oz	16.2	8.0	77	1.3	39	0	0,9	3.4	14	0
Şeker	10 lb.	51,7	34.9	0	0	0	0	0	0	0	0
Mısır Şurubu	24 oz.	13.7	14.7	0	0.5	74	0	0	0	5	0
Melaslar	18 oz.	13.6	9.0	0	10.3	244	0	1.9	7.5	146	0
Çilek Konserveleri	1 kg	20.5	6.4	11	0.4	7	0.2	0.2	0.4	3	0

Besinlerin tümü fiyata göre normalleştirildiği için hedefimiz sadece yiyeceklerin toplamını en aza indirmektir.

1944'te Stigler en iyi cevabı hesaplayarak üzgün olduğunu ifade etti:

...doğrusal koşullara tabi bir doğrusal fonksiyonun minimum değerini bulmak için doğrudan bir yöntem olmadığı anlaşılıyor.

1939 dolar ile yıllık 39, 93 dolarlık bir diyet buldu. 1947'de, Jack Laderman en uygun çözümü belirlemek için tek yönlü bir yöntem kullandı (o sırada yeni bir icattı). Masa başında çalışan dokuz çalışanının yanıta ulaşması 120 iş günü sürdü.

Doğrusal çözücü kullanarak çözüm

Aşağıdaki bölümlerde Stigler diyet sorununu çözen bir program sunulmaktadır.

Doğrusal çözücü sarmalayıcıyı içe aktarma

Aşağıda gösterildiği gibi, [GLOP](/optimization/mip/glop0 doğrusal çözücü) için bir arayüz olan VEYA-Araçlar doğrusal çözücü sarmalayıcıyı içe aktarın.

Python

from ortools.linear_solver import pywraplp

C++

#include <array>
#include <memory>
#include <string>
#include <utility>  // std::pair
#include <vector>

#include "absl/flags/flag.h"
#include "absl/log/flags.h"
#include "ortools/base/init_google.h"
#include "ortools/base/logging.h"
#include "ortools/linear_solver/linear_solver.h"

Java

import com.google.ortools.Loader;
import com.google.ortools.linearsolver.MPConstraint;
import com.google.ortools.linearsolver.MPObjective;
import com.google.ortools.linearsolver.MPSolver;
import com.google.ortools.linearsolver.MPVariable;
import java.util.ArrayList;
import java.util.List;

C#

using System;
using System.Collections.Generic;
using Google.OrTools.LinearSolver;

Problemin verileri

Aşağıdaki kod, herhangi bir çözümde minimum besin gereksinimleri için bir nutrients dizisi ve besin verileri tablosu için bir data dizisi oluşturur.

Python

# Nutrient minimums.
nutrients = [
    ["Calories (kcal)", 3],
    ["Protein (g)", 70],
    ["Calcium (g)", 0.8],
    ["Iron (mg)", 12],
    ["Vitamin A (KIU)", 5],
    ["Vitamin B1 (mg)", 1.8],
    ["Vitamin B2 (mg)", 2.7],
    ["Niacin (mg)", 18],
    ["Vitamin C (mg)", 75],
]

# Commodity, Unit, 1939 price (cents), Calories (kcal), Protein (g),
# Calcium (g), Iron (mg), Vitamin A (KIU), Vitamin B1 (mg), Vitamin B2 (mg),
# Niacin (mg), Vitamin C (mg)
data = [
    # fmt: off
  ['Wheat Flour (Enriched)', '10 lb.', 36, 44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0],
  ['Macaroni', '1 lb.', 14.1, 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0],
  ['Wheat Cereal (Enriched)', '28 oz.', 24.2, 11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0],
  ['Corn Flakes', '8 oz.', 7.1, 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0],
  ['Corn Meal', '1 lb.', 4.6, 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0],
  ['Hominy Grits', '24 oz.', 8.5, 28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0],
  ['Rice', '1 lb.', 7.5, 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0],
  ['Rolled Oats', '1 lb.', 7.1, 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0],
  ['White Bread (Enriched)', '1 lb.', 7.9, 15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0],
  ['Whole Wheat Bread', '1 lb.', 9.1, 12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0],
  ['Rye Bread', '1 lb.', 9.1, 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0],
  ['Pound Cake', '1 lb.', 24.8, 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0],
  ['Soda Crackers', '1 lb.', 15.1, 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0],
  ['Milk', '1 qt.', 11, 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177],
  ['Evaporated Milk (can)', '14.5 oz.', 6.7, 8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60],
  ['Butter', '1 lb.', 30.8, 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0],
  ['Oleomargarine', '1 lb.', 16.1, 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0],
  ['Eggs', '1 doz.', 32.6, 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0],
  ['Cheese (Cheddar)', '1 lb.', 24.2, 7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0],
  ['Cream', '1/2 pt.', 14.1, 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17],
  ['Peanut Butter', '1 lb.', 17.9, 15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0],
  ['Mayonnaise', '1/2 pt.', 16.7, 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0],
  ['Crisco', '1 lb.', 20.3, 20.1, 0, 0, 0, 0, 0, 0, 0, 0],
  ['Lard', '1 lb.', 9.8, 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0],
  ['Sirloin Steak', '1 lb.', 39.6, 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0],
  ['Round Steak', '1 lb.', 36.4, 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0],
  ['Rib Roast', '1 lb.', 29.2, 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0],
  ['Chuck Roast', '1 lb.', 22.6, 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0],
  ['Plate', '1 lb.', 14.6, 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0],
  ['Liver (Beef)', '1 lb.', 26.8, 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525],
  ['Leg of Lamb', '1 lb.', 27.6, 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0],
  ['Lamb Chops (Rib)', '1 lb.', 36.6, 3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0],
  ['Pork Chops', '1 lb.', 30.7, 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0],
  ['Pork Loin Roast', '1 lb.', 24.2, 4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0],
  ['Bacon', '1 lb.', 25.6, 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0],
  ['Ham, smoked', '1 lb.', 27.4, 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0],
  ['Salt Pork', '1 lb.', 16, 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0],
  ['Roasting Chicken', '1 lb.', 30.3, 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46],
  ['Veal Cutlets', '1 lb.', 42.3, 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0],
  ['Salmon, Pink (can)', '16 oz.', 13, 5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0],
  ['Apples', '1 lb.', 4.4, 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544],
  ['Bananas', '1 lb.', 6.1, 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498],
  ['Lemons', '1 doz.', 26, 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952],
  ['Oranges', '1 doz.', 30.9, 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998],
  ['Green Beans', '1 lb.', 7.1, 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862],
  ['Cabbage', '1 lb.', 3.7, 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369],
  ['Carrots', '1 bunch', 4.7, 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608],
  ['Celery', '1 stalk', 7.3, 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313],
  ['Lettuce', '1 head', 8.2, 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449],
  ['Onions', '1 lb.', 3.6, 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184],
  ['Potatoes', '15 lb.', 34, 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522],
  ['Spinach', '1 lb.', 8.1, 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755],
  ['Sweet Potatoes', '1 lb.', 5.1, 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912],
  ['Peaches (can)', 'No. 2 1/2', 16.8, 3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196],
  ['Pears (can)', 'No. 2 1/2', 20.4, 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81],
  ['Pineapple (can)', 'No. 2 1/2', 21.3, 2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399],
  ['Asparagus (can)', 'No. 2', 27.7, 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272],
  ['Green Beans (can)', 'No. 2', 10, 1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431],
  ['Pork and Beans (can)', '16 oz.', 7.1, 7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0],
  ['Corn (can)', 'No. 2', 10.4, 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218],
  ['Peas (can)', 'No. 2', 13.8, 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370],
  ['Tomatoes (can)', 'No. 2', 8.6, 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253],
  ['Tomato Soup (can)', '10 1/2 oz.', 7.6, 1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862],
  ['Peaches, Dried', '1 lb.', 15.7, 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57],
  ['Prunes, Dried', '1 lb.', 9, 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257],
  ['Raisins, Dried', '15 oz.', 9.4, 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136],
  ['Peas, Dried', '1 lb.', 7.9, 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0],
  ['Lima Beans, Dried', '1 lb.', 8.9, 17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0],
  ['Navy Beans, Dried', '1 lb.', 5.9, 26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0],
  ['Coffee', '1 lb.', 22.4, 0, 0, 0, 0, 0, 4, 5.1, 50, 0],
  ['Tea', '1/4 lb.', 17.4, 0, 0, 0, 0, 0, 0, 2.3, 42, 0],
  ['Cocoa', '8 oz.', 8.6, 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0],
  ['Chocolate', '8 oz.', 16.2, 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0],
  ['Sugar', '10 lb.', 51.7, 34.9, 0, 0, 0, 0, 0, 0, 0, 0],
  ['Corn Syrup', '24 oz.', 13.7, 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0],
  ['Molasses', '18 oz.', 13.6, 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0],
  ['Strawberry Preserves', '1 lb.', 20.5, 6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0],
    # fmt: on
]

C++

// Nutrient minimums.
const std::vector<std::pair<std::string, double>> nutrients = {
    {"Calories (kcal)", 3.0}, {"Protein (g)", 70.0},
    {"Calcium (g)", 0.8},     {"Iron (mg)", 12.0},
    {"Vitamin A (kIU)", 5.0}, {"Vitamin B1 (mg)", 1.8},
    {"Vitamin B2 (mg)", 2.7}, {"Niacin (mg)", 18.0},
    {"Vitamin C (mg)", 75.0}};

struct Commodity {
  std::string name;  //!< Commodity name
  std::string unit;  //!< Unit
  double price;      //!< 1939 price per unit (cents)
  //! Calories (kcal),
  //! Protein (g),
  //! Calcium (g),
  //! Iron (mg),
  //! Vitamin A (kIU),
  //! Vitamin B1 (mg),
  //! Vitamin B2 (mg),
  //! Niacin (mg),
  //! Vitamin C (mg)
  std::array<double, 9> nutrients;
};

std::vector<Commodity> data = {
    {"Wheat Flour (Enriched)",
     "10 lb.",
     36,
     {44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}},
    {"Macaroni", "1 lb.", 14.1, {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}},
    {"Wheat Cereal (Enriched)",
     "28 oz.",
     24.2,
     {11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}},
    {"Corn Flakes", "8 oz.", 7.1, {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}},
    {"Corn Meal",
     "1 lb.",
     4.6,
     {36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}},
    {"Hominy Grits",
     "24 oz.",
     8.5,
     {28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}},
    {"Rice", "1 lb.", 7.5, {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}},
    {"Rolled Oats", "1 lb.", 7.1, {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}},
    {"White Bread (Enriched)",
     "1 lb.",
     7.9,
     {15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}},
    {"Whole Wheat Bread",
     "1 lb.",
     9.1,
     {12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}},
    {"Rye Bread", "1 lb.", 9.1, {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}},
    {"Pound Cake", "1 lb.", 24.8, {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}},
    {"Soda Crackers", "1 lb.", 15.1, {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}},
    {"Milk", "1 qt.", 11, {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}},
    {"Evaporated Milk (can)",
     "14.5 oz.",
     6.7,
     {8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}},
    {"Butter", "1 lb.", 30.8, {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}},
    {"Oleomargarine", "1 lb.", 16.1, {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}},
    {"Eggs", "1 doz.", 32.6, {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}},
    {"Cheese (Cheddar)",
     "1 lb.",
     24.2,
     {7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}},
    {"Cream", "1/2 pt.", 14.1, {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}},
    {"Peanut Butter",
     "1 lb.",
     17.9,
     {15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}},
    {"Mayonnaise", "1/2 pt.", 16.7, {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}},
    {"Crisco", "1 lb.", 20.3, {20.1, 0, 0, 0, 0, 0, 0, 0, 0}},
    {"Lard", "1 lb.", 9.8, {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}},
    {"Sirloin Steak",
     "1 lb.",
     39.6,
     {2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}},
    {"Round Steak", "1 lb.", 36.4, {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}},
    {"Rib Roast", "1 lb.", 29.2, {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}},
    {"Chuck Roast", "1 lb.", 22.6, {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}},
    {"Plate", "1 lb.", 14.6, {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}},
    {"Liver (Beef)",
     "1 lb.",
     26.8,
     {2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}},
    {"Leg of Lamb", "1 lb.", 27.6, {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}},
    {"Lamb Chops (Rib)",
     "1 lb.",
     36.6,
     {3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}},
    {"Pork Chops", "1 lb.", 30.7, {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}},
    {"Pork Loin Roast",
     "1 lb.",
     24.2,
     {4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}},
    {"Bacon", "1 lb.", 25.6, {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}},
    {"Ham, smoked", "1 lb.", 27.4, {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}},
    {"Salt Pork", "1 lb.", 16, {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}},
    {"Roasting Chicken",
     "1 lb.",
     30.3,
     {1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}},
    {"Veal Cutlets", "1 lb.", 42.3, {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}},
    {"Salmon, Pink (can)",
     "16 oz.",
     13,
     {5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}},
    {"Apples", "1 lb.", 4.4, {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}},
    {"Bananas", "1 lb.", 6.1, {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}},
    {"Lemons", "1 doz.", 26, {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}},
    {"Oranges", "1 doz.", 30.9, {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}},
    {"Green Beans", "1 lb.", 7.1, {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}},
    {"Cabbage", "1 lb.", 3.7, {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}},
    {"Carrots", "1 bunch", 4.7, {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}},
    {"Celery", "1 stalk", 7.3, {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}},
    {"Lettuce", "1 head", 8.2, {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}},
    {"Onions", "1 lb.", 3.6, {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}},
    {"Potatoes",
     "15 lb.",
     34,
     {14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}},
    {"Spinach", "1 lb.", 8.1, {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}},
    {"Sweet Potatoes",
     "1 lb.",
     5.1,
     {9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}},
    {"Peaches (can)",
     "No. 2 1/2",
     16.8,
     {3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}},
    {"Pears (can)",
     "No. 2 1/2",
     20.4,
     {3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}},
    {"Pineapple (can)",
     "No. 2 1/2",
     21.3,
     {2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}},
    {"Asparagus (can)",
     "No. 2",
     27.7,
     {0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}},
    {"Green Beans (can)",
     "No. 2",
     10,
     {1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}},
    {"Pork and Beans (can)",
     "16 oz.",
     7.1,
     {7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}},
    {"Corn (can)", "No. 2", 10.4, {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}},
    {"Peas (can)",
     "No. 2",
     13.8,
     {2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}},
    {"Tomatoes (can)",
     "No. 2",
     8.6,
     {1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}},
    {"Tomato Soup (can)",
     "10 1/2 oz.",
     7.6,
     {1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}},
    {"Peaches, Dried",
     "1 lb.",
     15.7,
     {8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}},
    {"Prunes, Dried",
     "1 lb.",
     9,
     {12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}},
    {"Raisins, Dried",
     "15 oz.",
     9.4,
     {13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}},
    {"Peas, Dried",
     "1 lb.",
     7.9,
     {20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}},
    {"Lima Beans, Dried",
     "1 lb.",
     8.9,
     {17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}},
    {"Navy Beans, Dried",
     "1 lb.",
     5.9,
     {26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}},
    {"Coffee", "1 lb.", 22.4, {0, 0, 0, 0, 0, 4, 5.1, 50, 0}},
    {"Tea", "1/4 lb.", 17.4, {0, 0, 0, 0, 0, 0, 2.3, 42, 0}},
    {"Cocoa", "8 oz.", 8.6, {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}},
    {"Chocolate", "8 oz.", 16.2, {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}},
    {"Sugar", "10 lb.", 51.7, {34.9, 0, 0, 0, 0, 0, 0, 0, 0}},
    {"Corn Syrup", "24 oz.", 13.7, {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}},
    {"Molasses", "18 oz.", 13.6, {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}},
    {"Strawberry Preserves",
     "1 lb.",
     20.5,
     {6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}}};

Java

// Nutrient minimums.
List<Object[]> nutrients = new ArrayList<>();
nutrients.add(new Object[] {"Calories (kcal)", 3.0});
nutrients.add(new Object[] {"Protein (g)", 70.0});
nutrients.add(new Object[] {"Calcium (g)", 0.8});
nutrients.add(new Object[] {"Iron (mg)", 12.0});
nutrients.add(new Object[] {"Vitamin A (kIU)", 5.0});
nutrients.add(new Object[] {"Vitamin B1 (mg)", 1.8});
nutrients.add(new Object[] {"Vitamin B2 (mg)", 2.7});
nutrients.add(new Object[] {"Niacin (mg)", 18.0});
nutrients.add(new Object[] {"Vitamin C (mg)", 75.0});

List<Object[]> data = new ArrayList<>();
data.add(new Object[] {"Wheat Flour (Enriched)", "10 lb.", 36,
    new double[] {44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}});
data.add(new Object[] {
    "Macaroni", "1 lb.", 14.1, new double[] {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}});
data.add(new Object[] {"Wheat Cereal (Enriched)", "28 oz.", 24.2,
    new double[] {11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}});
data.add(new Object[] {
    "Corn Flakes", "8 oz.", 7.1, new double[] {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}});
data.add(new Object[] {
    "Corn Meal", "1 lb.", 4.6, new double[] {36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}});
data.add(new Object[] {
    "Hominy Grits", "24 oz.", 8.5, new double[] {28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}});
data.add(
    new Object[] {"Rice", "1 lb.", 7.5, new double[] {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}});
data.add(new Object[] {
    "Rolled Oats", "1 lb.", 7.1, new double[] {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}});
data.add(new Object[] {"White Bread (Enriched)", "1 lb.", 7.9,
    new double[] {15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}});
data.add(new Object[] {"Whole Wheat Bread", "1 lb.", 9.1,
    new double[] {12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}});
data.add(new Object[] {
    "Rye Bread", "1 lb.", 9.1, new double[] {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}});
data.add(new Object[] {
    "Pound Cake", "1 lb.", 24.8, new double[] {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}});
data.add(new Object[] {
    "Soda Crackers", "1 lb.", 15.1, new double[] {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}});
data.add(
    new Object[] {"Milk", "1 qt.", 11, new double[] {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}});
data.add(new Object[] {"Evaporated Milk (can)", "14.5 oz.", 6.7,
    new double[] {8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}});
data.add(
    new Object[] {"Butter", "1 lb.", 30.8, new double[] {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}});
data.add(new Object[] {
    "Oleomargarine", "1 lb.", 16.1, new double[] {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}});
data.add(new Object[] {
    "Eggs", "1 doz.", 32.6, new double[] {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}});
data.add(new Object[] {"Cheese (Cheddar)", "1 lb.", 24.2,
    new double[] {7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}});
data.add(new Object[] {
    "Cream", "1/2 pt.", 14.1, new double[] {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}});
data.add(new Object[] {
    "Peanut Butter", "1 lb.", 17.9, new double[] {15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}});
data.add(new Object[] {
    "Mayonnaise", "1/2 pt.", 16.7, new double[] {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}});
data.add(new Object[] {"Crisco", "1 lb.", 20.3, new double[] {20.1, 0, 0, 0, 0, 0, 0, 0, 0}});
data.add(new Object[] {"Lard", "1 lb.", 9.8, new double[] {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}});
data.add(new Object[] {
    "Sirloin Steak", "1 lb.", 39.6, new double[] {2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}});
data.add(new Object[] {
    "Round Steak", "1 lb.", 36.4, new double[] {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}});
data.add(
    new Object[] {"Rib Roast", "1 lb.", 29.2, new double[] {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}});
data.add(new Object[] {
    "Chuck Roast", "1 lb.", 22.6, new double[] {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}});
data.add(
    new Object[] {"Plate", "1 lb.", 14.6, new double[] {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}});
data.add(new Object[] {"Liver (Beef)", "1 lb.", 26.8,
    new double[] {2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}});
data.add(new Object[] {
    "Leg of Lamb", "1 lb.", 27.6, new double[] {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}});
data.add(new Object[] {
    "Lamb Chops (Rib)", "1 lb.", 36.6, new double[] {3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}});
data.add(new Object[] {
    "Pork Chops", "1 lb.", 30.7, new double[] {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}});
data.add(new Object[] {
    "Pork Loin Roast", "1 lb.", 24.2, new double[] {4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}});
data.add(new Object[] {
    "Bacon", "1 lb.", 25.6, new double[] {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}});
data.add(new Object[] {
    "Ham, smoked", "1 lb.", 27.4, new double[] {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}});
data.add(new Object[] {
    "Salt Pork", "1 lb.", 16, new double[] {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}});
data.add(new Object[] {"Roasting Chicken", "1 lb.", 30.3,
    new double[] {1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}});
data.add(new Object[] {
    "Veal Cutlets", "1 lb.", 42.3, new double[] {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}});
data.add(new Object[] {
    "Salmon, Pink (can)", "16 oz.", 13, new double[] {5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}});
data.add(new Object[] {
    "Apples", "1 lb.", 4.4, new double[] {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}});
data.add(new Object[] {
    "Bananas", "1 lb.", 6.1, new double[] {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}});
data.add(
    new Object[] {"Lemons", "1 doz.", 26, new double[] {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}});
data.add(new Object[] {
    "Oranges", "1 doz.", 30.9, new double[] {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}});
data.add(new Object[] {
    "Green Beans", "1 lb.", 7.1, new double[] {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}});
data.add(new Object[] {
    "Cabbage", "1 lb.", 3.7, new double[] {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}});
data.add(new Object[] {
    "Carrots", "1 bunch", 4.7, new double[] {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}});
data.add(new Object[] {
    "Celery", "1 stalk", 7.3, new double[] {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}});
data.add(new Object[] {
    "Lettuce", "1 head", 8.2, new double[] {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}});
data.add(new Object[] {
    "Onions", "1 lb.", 3.6, new double[] {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}});
data.add(new Object[] {
    "Potatoes", "15 lb.", 34, new double[] {14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}});
data.add(new Object[] {
    "Spinach", "1 lb.", 8.1, new double[] {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}});
data.add(new Object[] {"Sweet Potatoes", "1 lb.", 5.1,
    new double[] {9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}});
data.add(new Object[] {"Peaches (can)", "No. 2 1/2", 16.8,
    new double[] {3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}});
data.add(new Object[] {
    "Pears (can)", "No. 2 1/2", 20.4, new double[] {3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}});
data.add(new Object[] {
    "Pineapple (can)", "No. 2 1/2", 21.3, new double[] {2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}});
data.add(new Object[] {"Asparagus (can)", "No. 2", 27.7,
    new double[] {0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}});
data.add(new Object[] {
    "Green Beans (can)", "No. 2", 10, new double[] {1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}});
data.add(new Object[] {"Pork and Beans (can)", "16 oz.", 7.1,
    new double[] {7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}});
data.add(new Object[] {
    "Corn (can)", "No. 2", 10.4, new double[] {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}});
data.add(new Object[] {
    "Peas (can)", "No. 2", 13.8, new double[] {2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}});
data.add(new Object[] {
    "Tomatoes (can)", "No. 2", 8.6, new double[] {1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}});
data.add(new Object[] {"Tomato Soup (can)", "10 1/2 oz.", 7.6,
    new double[] {1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}});
data.add(new Object[] {
    "Peaches, Dried", "1 lb.", 15.7, new double[] {8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}});
data.add(new Object[] {
    "Prunes, Dried", "1 lb.", 9, new double[] {12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}});
data.add(new Object[] {"Raisins, Dried", "15 oz.", 9.4,
    new double[] {13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}});
data.add(new Object[] {
    "Peas, Dried", "1 lb.", 7.9, new double[] {20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}});
data.add(new Object[] {"Lima Beans, Dried", "1 lb.", 8.9,
    new double[] {17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}});
data.add(new Object[] {"Navy Beans, Dried", "1 lb.", 5.9,
    new double[] {26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}});
data.add(new Object[] {"Coffee", "1 lb.", 22.4, new double[] {0, 0, 0, 0, 0, 4, 5.1, 50, 0}});
data.add(new Object[] {"Tea", "1/4 lb.", 17.4, new double[] {0, 0, 0, 0, 0, 0, 2.3, 42, 0}});
data.add(
    new Object[] {"Cocoa", "8 oz.", 8.6, new double[] {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}});
data.add(new Object[] {
    "Chocolate", "8 oz.", 16.2, new double[] {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}});
data.add(new Object[] {"Sugar", "10 lb.", 51.7, new double[] {34.9, 0, 0, 0, 0, 0, 0, 0, 0}});
data.add(new Object[] {
    "Corn Syrup", "24 oz.", 13.7, new double[] {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}});
data.add(new Object[] {
    "Molasses", "18 oz.", 13.6, new double[] {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}});
data.add(new Object[] {"Strawberry Preserves", "1 lb.", 20.5,
    new double[] {6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}});

C#

// Nutrient minimums.
(String Name, double Value)[] nutrients =
    new[] { ("Calories (kcal)", 3.0), ("Protein (g)", 70.0),    ("Calcium (g)", 0.8),
            ("Iron (mg)", 12.0),      ("Vitamin A (kIU)", 5.0), ("Vitamin B1 (mg)", 1.8),
            ("Vitamin B2 (mg)", 2.7), ("Niacin (mg)", 18.0),    ("Vitamin C (mg)", 75.0) };

(String Name, String Unit, double Price, double[] Nutrients)[] data = new[] {
    ("Wheat Flour (Enriched)", "10 lb.", 36, new double[] { 44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0 }),
    ("Macaroni", "1 lb.", 14.1, new double[] { 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0 }),
    ("Wheat Cereal (Enriched)", "28 oz.", 24.2, new double[] { 11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0 }),
    ("Corn Flakes", "8 oz.", 7.1, new double[] { 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0 }),
    ("Corn Meal", "1 lb.", 4.6, new double[] { 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0 }),
    ("Hominy Grits", "24 oz.", 8.5, new double[] { 28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0 }),
    ("Rice", "1 lb.", 7.5, new double[] { 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0 }),
    ("Rolled Oats", "1 lb.", 7.1, new double[] { 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0 }),
    ("White Bread (Enriched)", "1 lb.", 7.9, new double[] { 15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0 }),
    ("Whole Wheat Bread", "1 lb.", 9.1, new double[] { 12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0 }),
    ("Rye Bread", "1 lb.", 9.1, new double[] { 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0 }),
    ("Pound Cake", "1 lb.", 24.8, new double[] { 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0 }),
    ("Soda Crackers", "1 lb.", 15.1, new double[] { 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0 }),
    ("Milk", "1 qt.", 11, new double[] { 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177 }),
    ("Evaporated Milk (can)", "14.5 oz.", 6.7, new double[] { 8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60 }),
    ("Butter", "1 lb.", 30.8, new double[] { 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0 }),
    ("Oleomargarine", "1 lb.", 16.1, new double[] { 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0 }),
    ("Eggs", "1 doz.", 32.6, new double[] { 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0 }),
    ("Cheese (Cheddar)", "1 lb.", 24.2, new double[] { 7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0 }),
    ("Cream", "1/2 pt.", 14.1, new double[] { 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17 }),
    ("Peanut Butter", "1 lb.", 17.9, new double[] { 15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0 }),
    ("Mayonnaise", "1/2 pt.", 16.7, new double[] { 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0 }),
    ("Crisco", "1 lb.", 20.3, new double[] { 20.1, 0, 0, 0, 0, 0, 0, 0, 0 }),
    ("Lard", "1 lb.", 9.8, new double[] { 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0 }),
    ("Sirloin Steak", "1 lb.", 39.6, new double[] { 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0 }),
    ("Round Steak", "1 lb.", 36.4, new double[] { 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0 }),
    ("Rib Roast", "1 lb.", 29.2, new double[] { 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0 }),
    ("Chuck Roast", "1 lb.", 22.6, new double[] { 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0 }),
    ("Plate", "1 lb.", 14.6, new double[] { 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0 }),
    ("Liver (Beef)", "1 lb.", 26.8, new double[] { 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525 }),
    ("Leg of Lamb", "1 lb.", 27.6, new double[] { 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0 }),
    ("Lamb Chops (Rib)", "1 lb.", 36.6, new double[] { 3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0 }),
    ("Pork Chops", "1 lb.", 30.7, new double[] { 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0 }),
    ("Pork Loin Roast", "1 lb.", 24.2, new double[] { 4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0 }),
    ("Bacon", "1 lb.", 25.6, new double[] { 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0 }),
    ("Ham, smoked", "1 lb.", 27.4, new double[] { 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0 }),
    ("Salt Pork", "1 lb.", 16, new double[] { 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0 }),
    ("Roasting Chicken", "1 lb.", 30.3, new double[] { 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46 }),
    ("Veal Cutlets", "1 lb.", 42.3, new double[] { 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0 }),
    ("Salmon, Pink (can)", "16 oz.", 13, new double[] { 5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0 }),
    ("Apples", "1 lb.", 4.4, new double[] { 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544 }),
    ("Bananas", "1 lb.", 6.1, new double[] { 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498 }),
    ("Lemons", "1 doz.", 26, new double[] { 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952 }),
    ("Oranges", "1 doz.", 30.9, new double[] { 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998 }),
    ("Green Beans", "1 lb.", 7.1, new double[] { 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862 }),
    ("Cabbage", "1 lb.", 3.7, new double[] { 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369 }),
    ("Carrots", "1 bunch", 4.7, new double[] { 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608 }),
    ("Celery", "1 stalk", 7.3, new double[] { 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313 }),
    ("Lettuce", "1 head", 8.2, new double[] { 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449 }),
    ("Onions", "1 lb.", 3.6, new double[] { 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184 }),
    ("Potatoes", "15 lb.", 34, new double[] { 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522 }),
    ("Spinach", "1 lb.", 8.1, new double[] { 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755 }),
    ("Sweet Potatoes", "1 lb.", 5.1, new double[] { 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912 }),
    ("Peaches (can)", "No. 2 1/2", 16.8, new double[] { 3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196 }),
    ("Pears (can)", "No. 2 1/2", 20.4, new double[] { 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81 }),
    ("Pineapple (can)", "No. 2 1/2", 21.3, new double[] { 2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399 }),
    ("Asparagus (can)", "No. 2", 27.7, new double[] { 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272 }),
    ("Green Beans (can)", "No. 2", 10, new double[] { 1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431 }),
    ("Pork and Beans (can)", "16 oz.", 7.1, new double[] { 7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0 }),
    ("Corn (can)", "No. 2", 10.4, new double[] { 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218 }),
    ("Peas (can)", "No. 2", 13.8, new double[] { 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370 }),
    ("Tomatoes (can)", "No. 2", 8.6, new double[] { 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253 }),
    ("Tomato Soup (can)", "10 1/2 oz.", 7.6, new double[] { 1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862 }),
    ("Peaches, Dried", "1 lb.", 15.7, new double[] { 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57 }),
    ("Prunes, Dried", "1 lb.", 9, new double[] { 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257 }),
    ("Raisins, Dried", "15 oz.", 9.4, new double[] { 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136 }),
    ("Peas, Dried", "1 lb.", 7.9, new double[] { 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0 }),
    ("Lima Beans, Dried", "1 lb.", 8.9, new double[] { 17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0 }),
    ("Navy Beans, Dried", "1 lb.", 5.9, new double[] { 26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0 }),
    ("Coffee", "1 lb.", 22.4, new double[] { 0, 0, 0, 0, 0, 4, 5.1, 50, 0 }),
    ("Tea", "1/4 lb.", 17.4, new double[] { 0, 0, 0, 0, 0, 0, 2.3, 42, 0 }),
    ("Cocoa", "8 oz.", 8.6, new double[] { 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0 }),
    ("Chocolate", "8 oz.", 16.2, new double[] { 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0 }),
    ("Sugar", "10 lb.", 51.7, new double[] { 34.9, 0, 0, 0, 0, 0, 0, 0, 0 }),
    ("Corn Syrup", "24 oz.", 13.7, new double[] { 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0 }),
    ("Molasses", "18 oz.", 13.6, new double[] { 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0 }),
    ("Strawberry Preserves", "1 lb.", 20.5, new double[] { 6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0 })
};

LP çözücüyü tanımlama

Aşağıdaki kod MPsolver sarmalayıcısını örneklendirir.

Python

# Instantiate a Glop solver and naming it.
solver = pywraplp.Solver.CreateSolver("GLOP")
if not solver:
    return

C++

// Create the linear solver with the GLOP backend.
std::unique_ptr<MPSolver> solver(MPSolver::CreateSolver("GLOP"));

Java

// Create the linear solver with the GLOP backend.
MPSolver solver = MPSolver.createSolver("GLOP");
if (solver == null) {
  System.out.println("Could not create solver GLOP");
  return;
}

C#

// Create the linear solver with the GLOP backend.
Solver solver = Solver.CreateSolver("GLOP");
if (solver is null)
{
    return;
}

Değişkenleri oluşturma

Aşağıdaki kod, sorun için değişkenler oluşturur.

Python

# Declare an array to hold our variables.
foods = [solver.NumVar(0.0, solver.infinity(), item[0]) for item in data]

print("Number of variables =", solver.NumVariables())

C++

std::vector<MPVariable*> foods;
const double infinity = solver->infinity();
for (const Commodity& commodity : data) {
  foods.push_back(solver->MakeNumVar(0.0, infinity, commodity.name));
}
LOG(INFO) << "Number of variables = " << solver->NumVariables();

Java

double infinity = java.lang.Double.POSITIVE_INFINITY;
List<MPVariable> foods = new ArrayList<>();
for (int i = 0; i < data.size(); ++i) {
  foods.add(solver.makeNumVar(0.0, infinity, (String) data.get(i)[0]));
}
System.out.println("Number of variables = " + solver.numVariables());

C#

List<Variable> foods = new List<Variable>();
for (int i = 0; i < data.Length; ++i)
{
    foods.Add(solver.MakeNumVar(0.0, double.PositiveInfinity, data[i].Name));
}
Console.WriteLine($"Number of variables = {solver.NumVariables()}");

MakeNumVar yöntemi, tablonun her bir satırı için bir değişken (food[i]) oluşturur. Daha önce de belirtildiği gibi, besin verileri dolar başınadır. Yani food[i], i adlı ürüne harcanabilecek para miktarıdır.

Kısıtlamaları tanımlama

Stigler diyetinin kısıtlamaları, tüm gıdalar tarafından sağlanan besin öğelerinin toplam miktarının, en azından her besin öğesi için minimum gereksinim olmasını gerektirir. Daha sonra bu kısıtlamaları data ve nutrients dizilerini ve food[i] değişkenlerini içeren eşitsizlikler olarak yazacağız.

Birincisi, j yemeğinin dolar başına sağladığı i besin miktarının data[j][i+3] şeklindedir (besin verileri data öğesinin dördüncü sütununda başladığı için sütun endeksine 3 eklenir.) Yiyecek j için harcanacak para miktarı food[j] olduğundan, j adlı gıdanın sağladığı i besin miktarını\(data[j][i+3] \cdot food[j]\)içerir. Son olarak, i besin değeri için minimum gereksinim nutrients[i][1] olduğundan, i kısıtlamasını aşağıdaki gibi yazabiliriz:

\( \sum_{j} data[j][i+3] \cdot food[j] \geq nutrients[i][1] \;\;\;\;\; (1) \)

Aşağıdaki kod bu kısıtlamaları tanımlar.

Python

# Create the constraints, one per nutrient.
constraints = []
for i, nutrient in enumerate(nutrients):
    constraints.append(solver.Constraint(nutrient[1], solver.infinity()))
    for j, item in enumerate(data):
        constraints[i].SetCoefficient(foods[j], item[i + 3])

print("Number of constraints =", solver.NumConstraints())

C++

// Create the constraints, one per nutrient.
std::vector<MPConstraint*> constraints;
for (std::size_t i = 0; i < nutrients.size(); ++i) {
  constraints.push_back(
      solver->MakeRowConstraint(nutrients[i].second, infinity));
  for (std::size_t j = 0; j < data.size(); ++j) {
    constraints.back()->SetCoefficient(foods[j], data[j].nutrients[i]);
  }
}
LOG(INFO) << "Number of constraints = " << solver->NumConstraints();

Java

MPConstraint[] constraints = new MPConstraint[nutrients.size()];
for (int i = 0; i < nutrients.size(); ++i) {
  constraints[i] = solver.makeConstraint(
      (double) nutrients.get(i)[1], infinity, (String) nutrients.get(i)[0]);
  for (int j = 0; j < data.size(); ++j) {
    constraints[i].setCoefficient(foods.get(j), ((double[]) data.get(j)[3])[i]);
  }
  // constraints.add(constraint);
}
System.out.println("Number of constraints = " + solver.numConstraints());

C#

List<Constraint> constraints = new List<Constraint>();
for (int i = 0; i < nutrients.Length; ++i)
{
    Constraint constraint =
        solver.MakeConstraint(nutrients[i].Value, double.PositiveInfinity, nutrients[i].Name);
    for (int j = 0; j < data.Length; ++j)
    {
        constraint.SetCoefficient(foods[j], data[j].Nutrients[i]);
    }
    constraints.Add(constraint);
}
Console.WriteLine($"Number of constraints = {solver.NumConstraints()}");

Constraint Python yöntemi (MakeRowConstraint C++ yöntemine karşılık gelir), problem için kısıtlamalar oluşturur. Her i için, constraint(nutrients[i][1], solver.infinity)

Bu, food[j] değişkenlerinin (sonraki olarak tanımlanır) doğrusal kombinasyonunun nutrients[i][1] değerinden büyük veya bu değere eşit olduğu bir kısıtlama oluşturur. Doğrusal ifadenin katsayıları, SetCoefficient yöntemi ile aşağıdaki gibi tanımlanır: SetCoefficient(food[j], data[j][i+3]

Bu işlem, food[j] katsayısını data[j][i+3] olarak ayarlar.

Bunların tümünü bir araya getiren kod, yukarıdaki (1)'de açıklanan kısıtlamaları tanımlar.

Hedefi oluşturun

Aşağıdaki kod, bu problem için amaç işlevini tanımlar.

Python

# Objective function: Minimize the sum of (price-normalized) foods.
objective = solver.Objective()
for food in foods:
    objective.SetCoefficient(food, 1)
objective.SetMinimization()

C++

MPObjective* const objective = solver->MutableObjective();
for (size_t i = 0; i < data.size(); ++i) {
  objective->SetCoefficient(foods[i], 1);
}
objective->SetMinimization();

Java

MPObjective objective = solver.objective();
for (int i = 0; i < data.size(); ++i) {
  objective.setCoefficient(foods.get(i), 1);
}
objective.setMinimization();

C#

Objective objective = solver.Objective();
for (int i = 0; i < data.Length; ++i)
{
    objective.SetCoefficient(foods[i], 1);
}
objective.SetMinimization();

Hedef fonksiyon, yiyeceğin toplam maliyetidir. Bu da food[i] değişkenlerinin toplamıdır.

SetCoefficient yöntemi, hedef işlevinin katsayılarını ayarlar. Bu durumda, bu katsayıların tümü 1 olur. Son olarak SetMinimization bunu bir minimumlandırma problemi olarak tanımlar.

Çözücüyü çağır

Aşağıdaki kod çözücüyü çağırır.

Python

print(f"Solving with {solver.SolverVersion()}")
status = solver.Solve()

C++

const MPSolver::ResultStatus result_status = solver->Solve();

Java

final MPSolver.ResultStatus resultStatus = solver.solve();

C#

Solver.ResultStatus resultStatus = solver.Solve();

Glop, normal bir bilgisayarda sorunu 300 milisaniyeden kısa sürede çözer:

Çözümü görüntüleyin

Aşağıdaki kod çözümü gösterir.

Python

# Check that the problem has an optimal solution.
if status != solver.OPTIMAL:
    print("The problem does not have an optimal solution!")
    if status == solver.FEASIBLE:
        print("A potentially suboptimal solution was found.")
    else:
        print("The solver could not solve the problem.")
        exit(1)

# Display the amounts (in dollars) to purchase of each food.
nutrients_result = [0] * len(nutrients)
print("\nAnnual Foods:")
for i, food in enumerate(foods):
    if food.solution_value() > 0.0:
        print("{}: ${}".format(data[i][0], 365.0 * food.solution_value()))
        for j, _ in enumerate(nutrients):
            nutrients_result[j] += data[i][j + 3] * food.solution_value()
print("\nOptimal annual price: ${:.4f}".format(365.0 * objective.Value()))

print("\nNutrients per day:")
for i, nutrient in enumerate(nutrients):
    print(
        "{}: {:.2f} (min {})".format(nutrient[0], nutrients_result[i], nutrient[1])
    )

C++

// Check that the problem has an optimal solution.
if (result_status != MPSolver::OPTIMAL) {
  LOG(INFO) << "The problem does not have an optimal solution!";
  if (result_status == MPSolver::FEASIBLE) {
    LOG(INFO) << "A potentially suboptimal solution was found";
  } else {
    LOG(INFO) << "The solver could not solve the problem.";
    return;
  }
}

std::vector<double> nutrients_result(nutrients.size());
LOG(INFO) << "";
LOG(INFO) << "Annual Foods:";
for (std::size_t i = 0; i < data.size(); ++i) {
  if (foods[i]->solution_value() > 0.0) {
    LOG(INFO) << data[i].name << ": $"
              << std::to_string(365. * foods[i]->solution_value());
    for (std::size_t j = 0; j < nutrients.size(); ++j) {
      nutrients_result[j] +=
          data[i].nutrients[j] * foods[i]->solution_value();
    }
  }
}
LOG(INFO) << "";
LOG(INFO) << "Optimal annual price: $"
          << std::to_string(365. * objective->Value());
LOG(INFO) << "";
LOG(INFO) << "Nutrients per day:";
for (std::size_t i = 0; i < nutrients.size(); ++i) {
  LOG(INFO) << nutrients[i].first << ": "
            << std::to_string(nutrients_result[i]) << " (min "
            << std::to_string(nutrients[i].second) << ")";
}

Java

// Check that the problem has an optimal solution.
if (resultStatus != MPSolver.ResultStatus.OPTIMAL) {
  System.err.println("The problem does not have an optimal solution!");
  if (resultStatus == MPSolver.ResultStatus.FEASIBLE) {
    System.err.println("A potentially suboptimal solution was found.");
  } else {
    System.err.println("The solver could not solve the problem.");
    return;
  }
}

// Display the amounts (in dollars) to purchase of each food.
double[] nutrientsResult = new double[nutrients.size()];
System.out.println("\nAnnual Foods:");
for (int i = 0; i < foods.size(); ++i) {
  if (foods.get(i).solutionValue() > 0.0) {
    System.out.println((String) data.get(i)[0] + ": $" + 365 * foods.get(i).solutionValue());
    for (int j = 0; j < nutrients.size(); ++j) {
      nutrientsResult[j] += ((double[]) data.get(i)[3])[j] * foods.get(i).solutionValue();
    }
  }
}
System.out.println("\nOptimal annual price: $" + 365 * objective.value());

System.out.println("\nNutrients per day:");
for (int i = 0; i < nutrients.size(); ++i) {
  System.out.println(
      nutrients.get(i)[0] + ": " + nutrientsResult[i] + " (min " + nutrients.get(i)[1] + ")");
}

C#

// Check that the problem has an optimal solution.
if (resultStatus != Solver.ResultStatus.OPTIMAL)
{
    Console.WriteLine("The problem does not have an optimal solution!");
    if (resultStatus == Solver.ResultStatus.FEASIBLE)
    {
        Console.WriteLine("A potentially suboptimal solution was found.");
    }
    else
    {
        Console.WriteLine("The solver could not solve the problem.");
        return;
    }
}

// Display the amounts (in dollars) to purchase of each food.
double[] nutrientsResult = new double[nutrients.Length];
Console.WriteLine("\nAnnual Foods:");
for (int i = 0; i < foods.Count; ++i)
{
    if (foods[i].SolutionValue() > 0.0)
    {
        Console.WriteLine($"{data[i].Name}: ${365 * foods[i].SolutionValue():N2}");
        for (int j = 0; j < nutrients.Length; ++j)
        {
            nutrientsResult[j] += data[i].Nutrients[j] * foods[i].SolutionValue();
        }
    }
}
Console.WriteLine($"\nOptimal annual price: ${365 * objective.Value():N2}");

Console.WriteLine("\nNutrients per day:");
for (int i = 0; i < nutrients.Length; ++i)
{
    Console.WriteLine($"{nutrients[i].Name}: {nutrientsResult[i]:N2} (min {nutrients[i].Value})");
}

Programın sonucunu burada bulabilirsiniz.

make rpy_stigler_diet
"/usr/bin/python3.11" ortools/linear_solver/samples/stigler_diet.py
Number of variables = 77
Number of constraints = 9

Annual Foods:
Wheat Flour (Enriched): $10.774457511918223
Liver (Beef): $0.6907834111074193
Cabbage: $4.093268864842877
Spinach: $1.8277960703546996
Navy Beans, Dried: $22.275425687243036

Optimal annual price: $39.6617

Nutrients per day:
Calories (kcal): 3.00 (min 3)
Protein (g): 147.41 (min 70)
Calcium (g): 0.80 (min 0.8)
Iron (mg): 60.47 (min 12)
Vitamin A (KIU): 5.00 (min 5)
Vitamin B1 (mg): 4.12 (min 1.8)
Vitamin B2 (mg): 2.70 (min 2.7)
Niacin (mg): 27.32 (min 18)
Vitamin C (mg): 75.00 (min 75)

Advanced usage:
Problem solved in  1  milliseconds
Problem solved in  14  iterations

Program kodunu tamamlayın

Stigler diyet programının kodu aşağıda verilmiştir.

Python

"""The Stigler diet problem.

A description of the problem can be found here:
https://en.wikipedia.org/wiki/Stigler_diet.
"""
from ortools.linear_solver import pywraplp


def main():
    """Entry point of the program."""
    # Instantiate the data problem.
    # Nutrient minimums.
    nutrients = [
        ["Calories (kcal)", 3],
        ["Protein (g)", 70],
        ["Calcium (g)", 0.8],
        ["Iron (mg)", 12],
        ["Vitamin A (KIU)", 5],
        ["Vitamin B1 (mg)", 1.8],
        ["Vitamin B2 (mg)", 2.7],
        ["Niacin (mg)", 18],
        ["Vitamin C (mg)", 75],
    ]

    # Commodity, Unit, 1939 price (cents), Calories (kcal), Protein (g),
    # Calcium (g), Iron (mg), Vitamin A (KIU), Vitamin B1 (mg), Vitamin B2 (mg),
    # Niacin (mg), Vitamin C (mg)
    data = [
        # fmt: off
      ['Wheat Flour (Enriched)', '10 lb.', 36, 44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0],
      ['Macaroni', '1 lb.', 14.1, 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0],
      ['Wheat Cereal (Enriched)', '28 oz.', 24.2, 11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0],
      ['Corn Flakes', '8 oz.', 7.1, 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0],
      ['Corn Meal', '1 lb.', 4.6, 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0],
      ['Hominy Grits', '24 oz.', 8.5, 28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0],
      ['Rice', '1 lb.', 7.5, 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0],
      ['Rolled Oats', '1 lb.', 7.1, 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0],
      ['White Bread (Enriched)', '1 lb.', 7.9, 15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0],
      ['Whole Wheat Bread', '1 lb.', 9.1, 12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0],
      ['Rye Bread', '1 lb.', 9.1, 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0],
      ['Pound Cake', '1 lb.', 24.8, 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0],
      ['Soda Crackers', '1 lb.', 15.1, 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0],
      ['Milk', '1 qt.', 11, 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177],
      ['Evaporated Milk (can)', '14.5 oz.', 6.7, 8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60],
      ['Butter', '1 lb.', 30.8, 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0],
      ['Oleomargarine', '1 lb.', 16.1, 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0],
      ['Eggs', '1 doz.', 32.6, 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0],
      ['Cheese (Cheddar)', '1 lb.', 24.2, 7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0],
      ['Cream', '1/2 pt.', 14.1, 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17],
      ['Peanut Butter', '1 lb.', 17.9, 15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0],
      ['Mayonnaise', '1/2 pt.', 16.7, 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0],
      ['Crisco', '1 lb.', 20.3, 20.1, 0, 0, 0, 0, 0, 0, 0, 0],
      ['Lard', '1 lb.', 9.8, 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0],
      ['Sirloin Steak', '1 lb.', 39.6, 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0],
      ['Round Steak', '1 lb.', 36.4, 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0],
      ['Rib Roast', '1 lb.', 29.2, 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0],
      ['Chuck Roast', '1 lb.', 22.6, 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0],
      ['Plate', '1 lb.', 14.6, 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0],
      ['Liver (Beef)', '1 lb.', 26.8, 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525],
      ['Leg of Lamb', '1 lb.', 27.6, 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0],
      ['Lamb Chops (Rib)', '1 lb.', 36.6, 3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0],
      ['Pork Chops', '1 lb.', 30.7, 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0],
      ['Pork Loin Roast', '1 lb.', 24.2, 4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0],
      ['Bacon', '1 lb.', 25.6, 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0],
      ['Ham, smoked', '1 lb.', 27.4, 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0],
      ['Salt Pork', '1 lb.', 16, 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0],
      ['Roasting Chicken', '1 lb.', 30.3, 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46],
      ['Veal Cutlets', '1 lb.', 42.3, 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0],
      ['Salmon, Pink (can)', '16 oz.', 13, 5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0],
      ['Apples', '1 lb.', 4.4, 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544],
      ['Bananas', '1 lb.', 6.1, 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498],
      ['Lemons', '1 doz.', 26, 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952],
      ['Oranges', '1 doz.', 30.9, 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998],
      ['Green Beans', '1 lb.', 7.1, 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862],
      ['Cabbage', '1 lb.', 3.7, 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369],
      ['Carrots', '1 bunch', 4.7, 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608],
      ['Celery', '1 stalk', 7.3, 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313],
      ['Lettuce', '1 head', 8.2, 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449],
      ['Onions', '1 lb.', 3.6, 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184],
      ['Potatoes', '15 lb.', 34, 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522],
      ['Spinach', '1 lb.', 8.1, 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755],
      ['Sweet Potatoes', '1 lb.', 5.1, 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912],
      ['Peaches (can)', 'No. 2 1/2', 16.8, 3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196],
      ['Pears (can)', 'No. 2 1/2', 20.4, 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81],
      ['Pineapple (can)', 'No. 2 1/2', 21.3, 2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399],
      ['Asparagus (can)', 'No. 2', 27.7, 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272],
      ['Green Beans (can)', 'No. 2', 10, 1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431],
      ['Pork and Beans (can)', '16 oz.', 7.1, 7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0],
      ['Corn (can)', 'No. 2', 10.4, 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218],
      ['Peas (can)', 'No. 2', 13.8, 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370],
      ['Tomatoes (can)', 'No. 2', 8.6, 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253],
      ['Tomato Soup (can)', '10 1/2 oz.', 7.6, 1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862],
      ['Peaches, Dried', '1 lb.', 15.7, 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57],
      ['Prunes, Dried', '1 lb.', 9, 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257],
      ['Raisins, Dried', '15 oz.', 9.4, 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136],
      ['Peas, Dried', '1 lb.', 7.9, 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0],
      ['Lima Beans, Dried', '1 lb.', 8.9, 17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0],
      ['Navy Beans, Dried', '1 lb.', 5.9, 26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0],
      ['Coffee', '1 lb.', 22.4, 0, 0, 0, 0, 0, 4, 5.1, 50, 0],
      ['Tea', '1/4 lb.', 17.4, 0, 0, 0, 0, 0, 0, 2.3, 42, 0],
      ['Cocoa', '8 oz.', 8.6, 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0],
      ['Chocolate', '8 oz.', 16.2, 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0],
      ['Sugar', '10 lb.', 51.7, 34.9, 0, 0, 0, 0, 0, 0, 0, 0],
      ['Corn Syrup', '24 oz.', 13.7, 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0],
      ['Molasses', '18 oz.', 13.6, 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0],
      ['Strawberry Preserves', '1 lb.', 20.5, 6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0],
        # fmt: on
    ]

    # Instantiate a Glop solver and naming it.
    solver = pywraplp.Solver.CreateSolver("GLOP")
    if not solver:
        return

    # Declare an array to hold our variables.
    foods = [solver.NumVar(0.0, solver.infinity(), item[0]) for item in data]

    print("Number of variables =", solver.NumVariables())

    # Create the constraints, one per nutrient.
    constraints = []
    for i, nutrient in enumerate(nutrients):
        constraints.append(solver.Constraint(nutrient[1], solver.infinity()))
        for j, item in enumerate(data):
            constraints[i].SetCoefficient(foods[j], item[i + 3])

    print("Number of constraints =", solver.NumConstraints())

    # Objective function: Minimize the sum of (price-normalized) foods.
    objective = solver.Objective()
    for food in foods:
        objective.SetCoefficient(food, 1)
    objective.SetMinimization()

    print(f"Solving with {solver.SolverVersion()}")
    status = solver.Solve()

    # Check that the problem has an optimal solution.
    if status != solver.OPTIMAL:
        print("The problem does not have an optimal solution!")
        if status == solver.FEASIBLE:
            print("A potentially suboptimal solution was found.")
        else:
            print("The solver could not solve the problem.")
            exit(1)

    # Display the amounts (in dollars) to purchase of each food.
    nutrients_result = [0] * len(nutrients)
    print("\nAnnual Foods:")
    for i, food in enumerate(foods):
        if food.solution_value() > 0.0:
            print("{}: ${}".format(data[i][0], 365.0 * food.solution_value()))
            for j, _ in enumerate(nutrients):
                nutrients_result[j] += data[i][j + 3] * food.solution_value()
    print("\nOptimal annual price: ${:.4f}".format(365.0 * objective.Value()))

    print("\nNutrients per day:")
    for i, nutrient in enumerate(nutrients):
        print(
            "{}: {:.2f} (min {})".format(nutrient[0], nutrients_result[i], nutrient[1])
        )

    print("\nAdvanced usage:")
    print(f"Problem solved in {solver.wall_time():d} milliseconds")
    print(f"Problem solved in {solver.iterations():d} iterations")


if __name__ == "__main__":
    main()

C++

// The Stigler diet problem.
#include <array>
#include <memory>
#include <string>
#include <utility>  // std::pair
#include <vector>

#include "absl/flags/flag.h"
#include "absl/log/flags.h"
#include "ortools/base/init_google.h"
#include "ortools/base/logging.h"
#include "ortools/linear_solver/linear_solver.h"

namespace operations_research {
void StiglerDiet() {
  // Nutrient minimums.
  const std::vector<std::pair<std::string, double>> nutrients = {
      {"Calories (kcal)", 3.0}, {"Protein (g)", 70.0},
      {"Calcium (g)", 0.8},     {"Iron (mg)", 12.0},
      {"Vitamin A (kIU)", 5.0}, {"Vitamin B1 (mg)", 1.8},
      {"Vitamin B2 (mg)", 2.7}, {"Niacin (mg)", 18.0},
      {"Vitamin C (mg)", 75.0}};

  struct Commodity {
    std::string name;  //!< Commodity name
    std::string unit;  //!< Unit
    double price;      //!< 1939 price per unit (cents)
    //! Calories (kcal),
    //! Protein (g),
    //! Calcium (g),
    //! Iron (mg),
    //! Vitamin A (kIU),
    //! Vitamin B1 (mg),
    //! Vitamin B2 (mg),
    //! Niacin (mg),
    //! Vitamin C (mg)
    std::array<double, 9> nutrients;
  };

  std::vector<Commodity> data = {
      {"Wheat Flour (Enriched)",
       "10 lb.",
       36,
       {44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}},
      {"Macaroni", "1 lb.", 14.1, {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}},
      {"Wheat Cereal (Enriched)",
       "28 oz.",
       24.2,
       {11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}},
      {"Corn Flakes", "8 oz.", 7.1, {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}},
      {"Corn Meal",
       "1 lb.",
       4.6,
       {36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}},
      {"Hominy Grits",
       "24 oz.",
       8.5,
       {28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}},
      {"Rice", "1 lb.", 7.5, {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}},
      {"Rolled Oats", "1 lb.", 7.1, {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}},
      {"White Bread (Enriched)",
       "1 lb.",
       7.9,
       {15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}},
      {"Whole Wheat Bread",
       "1 lb.",
       9.1,
       {12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}},
      {"Rye Bread", "1 lb.", 9.1, {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}},
      {"Pound Cake", "1 lb.", 24.8, {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}},
      {"Soda Crackers", "1 lb.", 15.1, {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}},
      {"Milk", "1 qt.", 11, {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}},
      {"Evaporated Milk (can)",
       "14.5 oz.",
       6.7,
       {8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}},
      {"Butter", "1 lb.", 30.8, {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}},
      {"Oleomargarine", "1 lb.", 16.1, {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}},
      {"Eggs", "1 doz.", 32.6, {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}},
      {"Cheese (Cheddar)",
       "1 lb.",
       24.2,
       {7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}},
      {"Cream", "1/2 pt.", 14.1, {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}},
      {"Peanut Butter",
       "1 lb.",
       17.9,
       {15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}},
      {"Mayonnaise", "1/2 pt.", 16.7, {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}},
      {"Crisco", "1 lb.", 20.3, {20.1, 0, 0, 0, 0, 0, 0, 0, 0}},
      {"Lard", "1 lb.", 9.8, {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}},
      {"Sirloin Steak",
       "1 lb.",
       39.6,
       {2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}},
      {"Round Steak", "1 lb.", 36.4, {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}},
      {"Rib Roast", "1 lb.", 29.2, {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}},
      {"Chuck Roast", "1 lb.", 22.6, {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}},
      {"Plate", "1 lb.", 14.6, {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}},
      {"Liver (Beef)",
       "1 lb.",
       26.8,
       {2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}},
      {"Leg of Lamb", "1 lb.", 27.6, {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}},
      {"Lamb Chops (Rib)",
       "1 lb.",
       36.6,
       {3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}},
      {"Pork Chops", "1 lb.", 30.7, {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}},
      {"Pork Loin Roast",
       "1 lb.",
       24.2,
       {4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}},
      {"Bacon", "1 lb.", 25.6, {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}},
      {"Ham, smoked", "1 lb.", 27.4, {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}},
      {"Salt Pork", "1 lb.", 16, {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}},
      {"Roasting Chicken",
       "1 lb.",
       30.3,
       {1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}},
      {"Veal Cutlets", "1 lb.", 42.3, {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}},
      {"Salmon, Pink (can)",
       "16 oz.",
       13,
       {5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}},
      {"Apples", "1 lb.", 4.4, {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}},
      {"Bananas", "1 lb.", 6.1, {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}},
      {"Lemons", "1 doz.", 26, {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}},
      {"Oranges", "1 doz.", 30.9, {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}},
      {"Green Beans", "1 lb.", 7.1, {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}},
      {"Cabbage", "1 lb.", 3.7, {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}},
      {"Carrots", "1 bunch", 4.7, {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}},
      {"Celery", "1 stalk", 7.3, {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}},
      {"Lettuce", "1 head", 8.2, {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}},
      {"Onions", "1 lb.", 3.6, {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}},
      {"Potatoes",
       "15 lb.",
       34,
       {14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}},
      {"Spinach", "1 lb.", 8.1, {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}},
      {"Sweet Potatoes",
       "1 lb.",
       5.1,
       {9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}},
      {"Peaches (can)",
       "No. 2 1/2",
       16.8,
       {3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}},
      {"Pears (can)",
       "No. 2 1/2",
       20.4,
       {3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}},
      {"Pineapple (can)",
       "No. 2 1/2",
       21.3,
       {2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}},
      {"Asparagus (can)",
       "No. 2",
       27.7,
       {0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}},
      {"Green Beans (can)",
       "No. 2",
       10,
       {1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}},
      {"Pork and Beans (can)",
       "16 oz.",
       7.1,
       {7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}},
      {"Corn (can)", "No. 2", 10.4, {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}},
      {"Peas (can)",
       "No. 2",
       13.8,
       {2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}},
      {"Tomatoes (can)",
       "No. 2",
       8.6,
       {1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}},
      {"Tomato Soup (can)",
       "10 1/2 oz.",
       7.6,
       {1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}},
      {"Peaches, Dried",
       "1 lb.",
       15.7,
       {8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}},
      {"Prunes, Dried",
       "1 lb.",
       9,
       {12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}},
      {"Raisins, Dried",
       "15 oz.",
       9.4,
       {13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}},
      {"Peas, Dried",
       "1 lb.",
       7.9,
       {20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}},
      {"Lima Beans, Dried",
       "1 lb.",
       8.9,
       {17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}},
      {"Navy Beans, Dried",
       "1 lb.",
       5.9,
       {26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}},
      {"Coffee", "1 lb.", 22.4, {0, 0, 0, 0, 0, 4, 5.1, 50, 0}},
      {"Tea", "1/4 lb.", 17.4, {0, 0, 0, 0, 0, 0, 2.3, 42, 0}},
      {"Cocoa", "8 oz.", 8.6, {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}},
      {"Chocolate", "8 oz.", 16.2, {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}},
      {"Sugar", "10 lb.", 51.7, {34.9, 0, 0, 0, 0, 0, 0, 0, 0}},
      {"Corn Syrup", "24 oz.", 13.7, {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}},
      {"Molasses", "18 oz.", 13.6, {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}},
      {"Strawberry Preserves",
       "1 lb.",
       20.5,
       {6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}}};

  // Create the linear solver with the GLOP backend.
  std::unique_ptr<MPSolver> solver(MPSolver::CreateSolver("GLOP"));

  std::vector<MPVariable*> foods;
  const double infinity = solver->infinity();
  for (const Commodity& commodity : data) {
    foods.push_back(solver->MakeNumVar(0.0, infinity, commodity.name));
  }
  LOG(INFO) << "Number of variables = " << solver->NumVariables();

  // Create the constraints, one per nutrient.
  std::vector<MPConstraint*> constraints;
  for (std::size_t i = 0; i < nutrients.size(); ++i) {
    constraints.push_back(
        solver->MakeRowConstraint(nutrients[i].second, infinity));
    for (std::size_t j = 0; j < data.size(); ++j) {
      constraints.back()->SetCoefficient(foods[j], data[j].nutrients[i]);
    }
  }
  LOG(INFO) << "Number of constraints = " << solver->NumConstraints();

  MPObjective* const objective = solver->MutableObjective();
  for (size_t i = 0; i < data.size(); ++i) {
    objective->SetCoefficient(foods[i], 1);
  }
  objective->SetMinimization();

  const MPSolver::ResultStatus result_status = solver->Solve();

  // Check that the problem has an optimal solution.
  if (result_status != MPSolver::OPTIMAL) {
    LOG(INFO) << "The problem does not have an optimal solution!";
    if (result_status == MPSolver::FEASIBLE) {
      LOG(INFO) << "A potentially suboptimal solution was found";
    } else {
      LOG(INFO) << "The solver could not solve the problem.";
      return;
    }
  }

  std::vector<double> nutrients_result(nutrients.size());
  LOG(INFO) << "";
  LOG(INFO) << "Annual Foods:";
  for (std::size_t i = 0; i < data.size(); ++i) {
    if (foods[i]->solution_value() > 0.0) {
      LOG(INFO) << data[i].name << ": $"
                << std::to_string(365. * foods[i]->solution_value());
      for (std::size_t j = 0; j < nutrients.size(); ++j) {
        nutrients_result[j] +=
            data[i].nutrients[j] * foods[i]->solution_value();
      }
    }
  }
  LOG(INFO) << "";
  LOG(INFO) << "Optimal annual price: $"
            << std::to_string(365. * objective->Value());
  LOG(INFO) << "";
  LOG(INFO) << "Nutrients per day:";
  for (std::size_t i = 0; i < nutrients.size(); ++i) {
    LOG(INFO) << nutrients[i].first << ": "
              << std::to_string(nutrients_result[i]) << " (min "
              << std::to_string(nutrients[i].second) << ")";
  }

  LOG(INFO) << "";
  LOG(INFO) << "Advanced usage:";
  LOG(INFO) << "Problem solved in " << solver->wall_time() << " milliseconds";
  LOG(INFO) << "Problem solved in " << solver->iterations() << " iterations";
}
}  // namespace operations_research

int main(int argc, char** argv) {
  InitGoogle(argv[0], &argc, &argv, true);
  absl::SetFlag(&FLAGS_stderrthreshold, 0);
  operations_research::StiglerDiet();
  return EXIT_SUCCESS;
}

Java

// The Stigler diet problem.
package com.google.ortools.linearsolver.samples;
import com.google.ortools.Loader;
import com.google.ortools.linearsolver.MPConstraint;
import com.google.ortools.linearsolver.MPObjective;
import com.google.ortools.linearsolver.MPSolver;
import com.google.ortools.linearsolver.MPVariable;
import java.util.ArrayList;
import java.util.List;

/** Stigler diet example. */
public final class StiglerDiet {
  public static void main(String[] args) {
    Loader.loadNativeLibraries();
    // Nutrient minimums.
    List<Object[]> nutrients = new ArrayList<>();
    nutrients.add(new Object[] {"Calories (kcal)", 3.0});
    nutrients.add(new Object[] {"Protein (g)", 70.0});
    nutrients.add(new Object[] {"Calcium (g)", 0.8});
    nutrients.add(new Object[] {"Iron (mg)", 12.0});
    nutrients.add(new Object[] {"Vitamin A (kIU)", 5.0});
    nutrients.add(new Object[] {"Vitamin B1 (mg)", 1.8});
    nutrients.add(new Object[] {"Vitamin B2 (mg)", 2.7});
    nutrients.add(new Object[] {"Niacin (mg)", 18.0});
    nutrients.add(new Object[] {"Vitamin C (mg)", 75.0});

    List<Object[]> data = new ArrayList<>();
    data.add(new Object[] {"Wheat Flour (Enriched)", "10 lb.", 36,
        new double[] {44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}});
    data.add(new Object[] {
        "Macaroni", "1 lb.", 14.1, new double[] {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}});
    data.add(new Object[] {"Wheat Cereal (Enriched)", "28 oz.", 24.2,
        new double[] {11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}});
    data.add(new Object[] {
        "Corn Flakes", "8 oz.", 7.1, new double[] {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}});
    data.add(new Object[] {
        "Corn Meal", "1 lb.", 4.6, new double[] {36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}});
    data.add(new Object[] {
        "Hominy Grits", "24 oz.", 8.5, new double[] {28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}});
    data.add(
        new Object[] {"Rice", "1 lb.", 7.5, new double[] {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}});
    data.add(new Object[] {
        "Rolled Oats", "1 lb.", 7.1, new double[] {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}});
    data.add(new Object[] {"White Bread (Enriched)", "1 lb.", 7.9,
        new double[] {15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}});
    data.add(new Object[] {"Whole Wheat Bread", "1 lb.", 9.1,
        new double[] {12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}});
    data.add(new Object[] {
        "Rye Bread", "1 lb.", 9.1, new double[] {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}});
    data.add(new Object[] {
        "Pound Cake", "1 lb.", 24.8, new double[] {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}});
    data.add(new Object[] {
        "Soda Crackers", "1 lb.", 15.1, new double[] {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}});
    data.add(
        new Object[] {"Milk", "1 qt.", 11, new double[] {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}});
    data.add(new Object[] {"Evaporated Milk (can)", "14.5 oz.", 6.7,
        new double[] {8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}});
    data.add(
        new Object[] {"Butter", "1 lb.", 30.8, new double[] {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}});
    data.add(new Object[] {
        "Oleomargarine", "1 lb.", 16.1, new double[] {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}});
    data.add(new Object[] {
        "Eggs", "1 doz.", 32.6, new double[] {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}});
    data.add(new Object[] {"Cheese (Cheddar)", "1 lb.", 24.2,
        new double[] {7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}});
    data.add(new Object[] {
        "Cream", "1/2 pt.", 14.1, new double[] {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}});
    data.add(new Object[] {
        "Peanut Butter", "1 lb.", 17.9, new double[] {15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}});
    data.add(new Object[] {
        "Mayonnaise", "1/2 pt.", 16.7, new double[] {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}});
    data.add(new Object[] {"Crisco", "1 lb.", 20.3, new double[] {20.1, 0, 0, 0, 0, 0, 0, 0, 0}});
    data.add(new Object[] {"Lard", "1 lb.", 9.8, new double[] {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}});
    data.add(new Object[] {
        "Sirloin Steak", "1 lb.", 39.6, new double[] {2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}});
    data.add(new Object[] {
        "Round Steak", "1 lb.", 36.4, new double[] {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}});
    data.add(
        new Object[] {"Rib Roast", "1 lb.", 29.2, new double[] {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}});
    data.add(new Object[] {
        "Chuck Roast", "1 lb.", 22.6, new double[] {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}});
    data.add(
        new Object[] {"Plate", "1 lb.", 14.6, new double[] {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}});
    data.add(new Object[] {"Liver (Beef)", "1 lb.", 26.8,
        new double[] {2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}});
    data.add(new Object[] {
        "Leg of Lamb", "1 lb.", 27.6, new double[] {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}});
    data.add(new Object[] {
        "Lamb Chops (Rib)", "1 lb.", 36.6, new double[] {3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}});
    data.add(new Object[] {
        "Pork Chops", "1 lb.", 30.7, new double[] {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}});
    data.add(new Object[] {
        "Pork Loin Roast", "1 lb.", 24.2, new double[] {4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}});
    data.add(new Object[] {
        "Bacon", "1 lb.", 25.6, new double[] {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}});
    data.add(new Object[] {
        "Ham, smoked", "1 lb.", 27.4, new double[] {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}});
    data.add(new Object[] {
        "Salt Pork", "1 lb.", 16, new double[] {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}});
    data.add(new Object[] {"Roasting Chicken", "1 lb.", 30.3,
        new double[] {1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}});
    data.add(new Object[] {
        "Veal Cutlets", "1 lb.", 42.3, new double[] {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}});
    data.add(new Object[] {
        "Salmon, Pink (can)", "16 oz.", 13, new double[] {5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}});
    data.add(new Object[] {
        "Apples", "1 lb.", 4.4, new double[] {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}});
    data.add(new Object[] {
        "Bananas", "1 lb.", 6.1, new double[] {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}});
    data.add(
        new Object[] {"Lemons", "1 doz.", 26, new double[] {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}});
    data.add(new Object[] {
        "Oranges", "1 doz.", 30.9, new double[] {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}});
    data.add(new Object[] {
        "Green Beans", "1 lb.", 7.1, new double[] {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}});
    data.add(new Object[] {
        "Cabbage", "1 lb.", 3.7, new double[] {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}});
    data.add(new Object[] {
        "Carrots", "1 bunch", 4.7, new double[] {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}});
    data.add(new Object[] {
        "Celery", "1 stalk", 7.3, new double[] {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}});
    data.add(new Object[] {
        "Lettuce", "1 head", 8.2, new double[] {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}});
    data.add(new Object[] {
        "Onions", "1 lb.", 3.6, new double[] {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}});
    data.add(new Object[] {
        "Potatoes", "15 lb.", 34, new double[] {14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}});
    data.add(new Object[] {
        "Spinach", "1 lb.", 8.1, new double[] {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}});
    data.add(new Object[] {"Sweet Potatoes", "1 lb.", 5.1,
        new double[] {9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}});
    data.add(new Object[] {"Peaches (can)", "No. 2 1/2", 16.8,
        new double[] {3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}});
    data.add(new Object[] {
        "Pears (can)", "No. 2 1/2", 20.4, new double[] {3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}});
    data.add(new Object[] {
        "Pineapple (can)", "No. 2 1/2", 21.3, new double[] {2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}});
    data.add(new Object[] {"Asparagus (can)", "No. 2", 27.7,
        new double[] {0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}});
    data.add(new Object[] {
        "Green Beans (can)", "No. 2", 10, new double[] {1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}});
    data.add(new Object[] {"Pork and Beans (can)", "16 oz.", 7.1,
        new double[] {7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}});
    data.add(new Object[] {
        "Corn (can)", "No. 2", 10.4, new double[] {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}});
    data.add(new Object[] {
        "Peas (can)", "No. 2", 13.8, new double[] {2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}});
    data.add(new Object[] {
        "Tomatoes (can)", "No. 2", 8.6, new double[] {1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}});
    data.add(new Object[] {"Tomato Soup (can)", "10 1/2 oz.", 7.6,
        new double[] {1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}});
    data.add(new Object[] {
        "Peaches, Dried", "1 lb.", 15.7, new double[] {8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}});
    data.add(new Object[] {
        "Prunes, Dried", "1 lb.", 9, new double[] {12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}});
    data.add(new Object[] {"Raisins, Dried", "15 oz.", 9.4,
        new double[] {13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}});
    data.add(new Object[] {
        "Peas, Dried", "1 lb.", 7.9, new double[] {20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}});
    data.add(new Object[] {"Lima Beans, Dried", "1 lb.", 8.9,
        new double[] {17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}});
    data.add(new Object[] {"Navy Beans, Dried", "1 lb.", 5.9,
        new double[] {26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}});
    data.add(new Object[] {"Coffee", "1 lb.", 22.4, new double[] {0, 0, 0, 0, 0, 4, 5.1, 50, 0}});
    data.add(new Object[] {"Tea", "1/4 lb.", 17.4, new double[] {0, 0, 0, 0, 0, 0, 2.3, 42, 0}});
    data.add(
        new Object[] {"Cocoa", "8 oz.", 8.6, new double[] {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}});
    data.add(new Object[] {
        "Chocolate", "8 oz.", 16.2, new double[] {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}});
    data.add(new Object[] {"Sugar", "10 lb.", 51.7, new double[] {34.9, 0, 0, 0, 0, 0, 0, 0, 0}});
    data.add(new Object[] {
        "Corn Syrup", "24 oz.", 13.7, new double[] {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}});
    data.add(new Object[] {
        "Molasses", "18 oz.", 13.6, new double[] {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}});
    data.add(new Object[] {"Strawberry Preserves", "1 lb.", 20.5,
        new double[] {6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}});


    // Create the linear solver with the GLOP backend.
    MPSolver solver = MPSolver.createSolver("GLOP");
    if (solver == null) {
      System.out.println("Could not create solver GLOP");
      return;
    }

    double infinity = java.lang.Double.POSITIVE_INFINITY;
    List<MPVariable> foods = new ArrayList<>();
    for (int i = 0; i < data.size(); ++i) {
      foods.add(solver.makeNumVar(0.0, infinity, (String) data.get(i)[0]));
    }
    System.out.println("Number of variables = " + solver.numVariables());

    MPConstraint[] constraints = new MPConstraint[nutrients.size()];
    for (int i = 0; i < nutrients.size(); ++i) {
      constraints[i] = solver.makeConstraint(
          (double) nutrients.get(i)[1], infinity, (String) nutrients.get(i)[0]);
      for (int j = 0; j < data.size(); ++j) {
        constraints[i].setCoefficient(foods.get(j), ((double[]) data.get(j)[3])[i]);
      }
      // constraints.add(constraint);
    }
    System.out.println("Number of constraints = " + solver.numConstraints());

    MPObjective objective = solver.objective();
    for (int i = 0; i < data.size(); ++i) {
      objective.setCoefficient(foods.get(i), 1);
    }
    objective.setMinimization();

    final MPSolver.ResultStatus resultStatus = solver.solve();

    // Check that the problem has an optimal solution.
    if (resultStatus != MPSolver.ResultStatus.OPTIMAL) {
      System.err.println("The problem does not have an optimal solution!");
      if (resultStatus == MPSolver.ResultStatus.FEASIBLE) {
        System.err.println("A potentially suboptimal solution was found.");
      } else {
        System.err.println("The solver could not solve the problem.");
        return;
      }
    }

    // Display the amounts (in dollars) to purchase of each food.
    double[] nutrientsResult = new double[nutrients.size()];
    System.out.println("\nAnnual Foods:");
    for (int i = 0; i < foods.size(); ++i) {
      if (foods.get(i).solutionValue() > 0.0) {
        System.out.println((String) data.get(i)[0] + ": $" + 365 * foods.get(i).solutionValue());
        for (int j = 0; j < nutrients.size(); ++j) {
          nutrientsResult[j] += ((double[]) data.get(i)[3])[j] * foods.get(i).solutionValue();
        }
      }
    }
    System.out.println("\nOptimal annual price: $" + 365 * objective.value());

    System.out.println("\nNutrients per day:");
    for (int i = 0; i < nutrients.size(); ++i) {
      System.out.println(
          nutrients.get(i)[0] + ": " + nutrientsResult[i] + " (min " + nutrients.get(i)[1] + ")");
    }

    System.out.println("\nAdvanced usage:");
    System.out.println("Problem solved in " + solver.wallTime() + " milliseconds");
    System.out.println("Problem solved in " + solver.iterations() + " iterations");
  }

  private StiglerDiet() {}
}

C#

// The Stigler diet problem.
using System;
using System.Collections.Generic;
using Google.OrTools.LinearSolver;

public class StiglerDiet
{
    static void Main()
    {
        // Nutrient minimums.
        (String Name, double Value)[] nutrients =
            new[] { ("Calories (kcal)", 3.0), ("Protein (g)", 70.0),    ("Calcium (g)", 0.8),
                    ("Iron (mg)", 12.0),      ("Vitamin A (kIU)", 5.0), ("Vitamin B1 (mg)", 1.8),
                    ("Vitamin B2 (mg)", 2.7), ("Niacin (mg)", 18.0),    ("Vitamin C (mg)", 75.0) };

        (String Name, String Unit, double Price, double[] Nutrients)[] data = new[] {
            ("Wheat Flour (Enriched)", "10 lb.", 36, new double[] { 44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0 }),
            ("Macaroni", "1 lb.", 14.1, new double[] { 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0 }),
            ("Wheat Cereal (Enriched)", "28 oz.", 24.2, new double[] { 11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0 }),
            ("Corn Flakes", "8 oz.", 7.1, new double[] { 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0 }),
            ("Corn Meal", "1 lb.", 4.6, new double[] { 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0 }),
            ("Hominy Grits", "24 oz.", 8.5, new double[] { 28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0 }),
            ("Rice", "1 lb.", 7.5, new double[] { 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0 }),
            ("Rolled Oats", "1 lb.", 7.1, new double[] { 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0 }),
            ("White Bread (Enriched)", "1 lb.", 7.9, new double[] { 15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0 }),
            ("Whole Wheat Bread", "1 lb.", 9.1, new double[] { 12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0 }),
            ("Rye Bread", "1 lb.", 9.1, new double[] { 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0 }),
            ("Pound Cake", "1 lb.", 24.8, new double[] { 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0 }),
            ("Soda Crackers", "1 lb.", 15.1, new double[] { 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0 }),
            ("Milk", "1 qt.", 11, new double[] { 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177 }),
            ("Evaporated Milk (can)", "14.5 oz.", 6.7, new double[] { 8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60 }),
            ("Butter", "1 lb.", 30.8, new double[] { 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0 }),
            ("Oleomargarine", "1 lb.", 16.1, new double[] { 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0 }),
            ("Eggs", "1 doz.", 32.6, new double[] { 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0 }),
            ("Cheese (Cheddar)", "1 lb.", 24.2, new double[] { 7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0 }),
            ("Cream", "1/2 pt.", 14.1, new double[] { 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17 }),
            ("Peanut Butter", "1 lb.", 17.9, new double[] { 15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0 }),
            ("Mayonnaise", "1/2 pt.", 16.7, new double[] { 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0 }),
            ("Crisco", "1 lb.", 20.3, new double[] { 20.1, 0, 0, 0, 0, 0, 0, 0, 0 }),
            ("Lard", "1 lb.", 9.8, new double[] { 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0 }),
            ("Sirloin Steak", "1 lb.", 39.6, new double[] { 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0 }),
            ("Round Steak", "1 lb.", 36.4, new double[] { 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0 }),
            ("Rib Roast", "1 lb.", 29.2, new double[] { 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0 }),
            ("Chuck Roast", "1 lb.", 22.6, new double[] { 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0 }),
            ("Plate", "1 lb.", 14.6, new double[] { 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0 }),
            ("Liver (Beef)", "1 lb.", 26.8, new double[] { 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525 }),
            ("Leg of Lamb", "1 lb.", 27.6, new double[] { 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0 }),
            ("Lamb Chops (Rib)", "1 lb.", 36.6, new double[] { 3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0 }),
            ("Pork Chops", "1 lb.", 30.7, new double[] { 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0 }),
            ("Pork Loin Roast", "1 lb.", 24.2, new double[] { 4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0 }),
            ("Bacon", "1 lb.", 25.6, new double[] { 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0 }),
            ("Ham, smoked", "1 lb.", 27.4, new double[] { 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0 }),
            ("Salt Pork", "1 lb.", 16, new double[] { 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0 }),
            ("Roasting Chicken", "1 lb.", 30.3, new double[] { 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46 }),
            ("Veal Cutlets", "1 lb.", 42.3, new double[] { 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0 }),
            ("Salmon, Pink (can)", "16 oz.", 13, new double[] { 5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0 }),
            ("Apples", "1 lb.", 4.4, new double[] { 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544 }),
            ("Bananas", "1 lb.", 6.1, new double[] { 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498 }),
            ("Lemons", "1 doz.", 26, new double[] { 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952 }),
            ("Oranges", "1 doz.", 30.9, new double[] { 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998 }),
            ("Green Beans", "1 lb.", 7.1, new double[] { 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862 }),
            ("Cabbage", "1 lb.", 3.7, new double[] { 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369 }),
            ("Carrots", "1 bunch", 4.7, new double[] { 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608 }),
            ("Celery", "1 stalk", 7.3, new double[] { 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313 }),
            ("Lettuce", "1 head", 8.2, new double[] { 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449 }),
            ("Onions", "1 lb.", 3.6, new double[] { 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184 }),
            ("Potatoes", "15 lb.", 34, new double[] { 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522 }),
            ("Spinach", "1 lb.", 8.1, new double[] { 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755 }),
            ("Sweet Potatoes", "1 lb.", 5.1, new double[] { 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912 }),
            ("Peaches (can)", "No. 2 1/2", 16.8, new double[] { 3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196 }),
            ("Pears (can)", "No. 2 1/2", 20.4, new double[] { 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81 }),
            ("Pineapple (can)", "No. 2 1/2", 21.3, new double[] { 2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399 }),
            ("Asparagus (can)", "No. 2", 27.7, new double[] { 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272 }),
            ("Green Beans (can)", "No. 2", 10, new double[] { 1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431 }),
            ("Pork and Beans (can)", "16 oz.", 7.1, new double[] { 7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0 }),
            ("Corn (can)", "No. 2", 10.4, new double[] { 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218 }),
            ("Peas (can)", "No. 2", 13.8, new double[] { 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370 }),
            ("Tomatoes (can)", "No. 2", 8.6, new double[] { 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253 }),
            ("Tomato Soup (can)", "10 1/2 oz.", 7.6, new double[] { 1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862 }),
            ("Peaches, Dried", "1 lb.", 15.7, new double[] { 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57 }),
            ("Prunes, Dried", "1 lb.", 9, new double[] { 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257 }),
            ("Raisins, Dried", "15 oz.", 9.4, new double[] { 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136 }),
            ("Peas, Dried", "1 lb.", 7.9, new double[] { 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0 }),
            ("Lima Beans, Dried", "1 lb.", 8.9, new double[] { 17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0 }),
            ("Navy Beans, Dried", "1 lb.", 5.9, new double[] { 26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0 }),
            ("Coffee", "1 lb.", 22.4, new double[] { 0, 0, 0, 0, 0, 4, 5.1, 50, 0 }),
            ("Tea", "1/4 lb.", 17.4, new double[] { 0, 0, 0, 0, 0, 0, 2.3, 42, 0 }),
            ("Cocoa", "8 oz.", 8.6, new double[] { 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0 }),
            ("Chocolate", "8 oz.", 16.2, new double[] { 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0 }),
            ("Sugar", "10 lb.", 51.7, new double[] { 34.9, 0, 0, 0, 0, 0, 0, 0, 0 }),
            ("Corn Syrup", "24 oz.", 13.7, new double[] { 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0 }),
            ("Molasses", "18 oz.", 13.6, new double[] { 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0 }),
            ("Strawberry Preserves", "1 lb.", 20.5, new double[] { 6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0 })
        };

        // Create the linear solver with the GLOP backend.
        Solver solver = Solver.CreateSolver("GLOP");
        if (solver is null)
        {
            return;
        }

        List<Variable> foods = new List<Variable>();
        for (int i = 0; i < data.Length; ++i)
        {
            foods.Add(solver.MakeNumVar(0.0, double.PositiveInfinity, data[i].Name));
        }
        Console.WriteLine($"Number of variables = {solver.NumVariables()}");

        List<Constraint> constraints = new List<Constraint>();
        for (int i = 0; i < nutrients.Length; ++i)
        {
            Constraint constraint =
                solver.MakeConstraint(nutrients[i].Value, double.PositiveInfinity, nutrients[i].Name);
            for (int j = 0; j < data.Length; ++j)
            {
                constraint.SetCoefficient(foods[j], data[j].Nutrients[i]);
            }
            constraints.Add(constraint);
        }
        Console.WriteLine($"Number of constraints = {solver.NumConstraints()}");

        Objective objective = solver.Objective();
        for (int i = 0; i < data.Length; ++i)
        {
            objective.SetCoefficient(foods[i], 1);
        }
        objective.SetMinimization();

        Solver.ResultStatus resultStatus = solver.Solve();

        // Check that the problem has an optimal solution.
        if (resultStatus != Solver.ResultStatus.OPTIMAL)
        {
            Console.WriteLine("The problem does not have an optimal solution!");
            if (resultStatus == Solver.ResultStatus.FEASIBLE)
            {
                Console.WriteLine("A potentially suboptimal solution was found.");
            }
            else
            {
                Console.WriteLine("The solver could not solve the problem.");
                return;
            }
        }

        // Display the amounts (in dollars) to purchase of each food.
        double[] nutrientsResult = new double[nutrients.Length];
        Console.WriteLine("\nAnnual Foods:");
        for (int i = 0; i < foods.Count; ++i)
        {
            if (foods[i].SolutionValue() > 0.0)
            {
                Console.WriteLine($"{data[i].Name}: ${365 * foods[i].SolutionValue():N2}");
                for (int j = 0; j < nutrients.Length; ++j)
                {
                    nutrientsResult[j] += data[i].Nutrients[j] * foods[i].SolutionValue();
                }
            }
        }
        Console.WriteLine($"\nOptimal annual price: ${365 * objective.Value():N2}");

        Console.WriteLine("\nNutrients per day:");
        for (int i = 0; i < nutrients.Length; ++i)
        {
            Console.WriteLine($"{nutrients[i].Name}: {nutrientsResult[i]:N2} (min {nutrients[i].Value})");
        }

        Console.WriteLine("\nAdvanced usage:");
        Console.WriteLine($"Problem solved in {solver.WallTime()} milliseconds");
        Console.WriteLine($"Problem solved in {solver.Iterations()} iterations");
    }
}