Nesta seção, mostramos como resolver um problema clássico chamado dieta Stigler (em inglês), nomeado em homenagem ao ganhador do prêmio Nobel da economia, George Stigler, que calculou uma maneira barata de atender às necessidades nutricionais básicas de acordo com um conjunto de alimentos. Ele apontou isso como um exercício matemático, e não como recomendações de alimentação, embora a noção de computação de nutrição ideal tenha surgido recentemente.
A dieta Stigler exigiu que estes requisitos mínimos fossem atendidos:
Lista de nutrientes
| Nutriente | Consumo diário recomendado |
|---|---|
| Calorias | 3.000 calorias |
| Proteína | 70 g |
| Cálcio | 0,8 grama |
| Ferro | 12 miligramas |
| Vitamina A | 5.000 interface |
| Tiamina (Vitamina B1) | 1,8 miligrama |
| Riboflavina (Vitamina B2) | 2,7 miligramas |
| Niacina | 18 miligramas |
| Ácido ascórbico (vitamina C) | 75 miligramas |
O conjunto de alimentos avaliado por Stigler foi um reflexo do tempo (1944). Os dados nutricionais abaixo são por dólar, não por unidade. Portanto, o objetivo é determinar quantos dólares gastar em cada alimento.
Lista de mercadorias
| Bens | Unidade | Preço para 1939 (centavos) | Calorias (kcal) | Proteínas (g) | Cálcio (g) | Ferro (mg) | Vitamina A (KIU) | Tiamina (mg) | Riboflavina (mg) | Niacina (mg) | Ácido ascórbico (mg) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Farinha de trigo (enriquecida) | 10 lb | 36 | 44,7 | 1411 | 2 | 365 | 0 | 55.4 | 33.3 | 441 | 0 |
| Mostarda | 0,45 kg | 14.1 | 11.6 | 418 | 0.7 | 54 | 0 | 3.2 | 1.9 | 68 | 0 |
| Cereal de trigo (enriquecido) | 800 g | 24.2 | 11.8 | 377 | 14.4 | 175 | 0 | 14.4 | 8.8 | 114 | 0 |
| Flocos de milho | 226,8 g | 7.1 | 11.4 | 252 | 0,1 | 56 | 0 | 13.5 | 2.3 | 68 | 0 |
| Milho | 0,45 kg | 4.6 | 36.0 | 897 | 1.7 | 99 | 30.9 | 17.4 | 7,9 | 106 | 0 |
| Grits de hominy | 605 g | 8.5 | 28.6 | 680 | 0,8 | 80 | 0 | 10.6 | 1.6 | 110 | 0 |
| Arroz | 0,45 kg | 7.5 | 21.2 | 460 | 0.6 | 41 | 0 | 2 | 4,8 | 60 | 0 |
| Aveia em flocos | 0,45 kg | 7.1 | 25,3 | 907 | 5.1 | 341 | 0 | 37.1 | 8.9 | 64 | 0 |
| White Bread (enriquecido) | 0,45 kg | 7,9 | 15.0 | 488 | 2.5 | 115 | 0 | 13.8 | 8.5 | 126 | 0 |
| Pão integral | 0,45 kg | 9.1 | 12.2 | 484 | 2.7 | 125 | 0 | 13.9 | 6.4 | 160 | 0 |
| Pão de centeio | 0,45 kg | 9.1 | 12.4 | 439 | 1.1 | 82 | 0 | 9.9 | 3 | 66 | 0 |
| Bolo de libra | 0,45 kg | 24,8 | 8.0 | 130 | 0.4 | 31 | 18,9 | 2.8 | 3 | 17 | 0 |
| Biscoitos de refrigerante | 0,45 kg | 15.1 | 12.5 | 288 | 0.5 | 50 | 0 | 0 | 0 | 0 | 0 |
| Leite | 1 qt. | 11 | 6.1 | 310 | 10.5 | 18 | 16.8 | 4 | 16 | 7 | 177 |
| Leite evaporado (lata) | 45,6 g | 6.7 | 8.4 | 422 | 15.1 | 9 | 26 | 3 | 23.5 | 11 | 60 |
| Manteiga | 0,45 kg | 30.8 | 10.8 | 9 | 0,2 | 3 | 44.2 | 0 | 0,2 | 2 | 0 |
| Oleomargarina | 0,45 kg | 16.1 | 20,6 | 17 | 0.6 | 6 | 55.8 | 0,2 | 0 | 0 | 0 |
| Ovos | 1 doz. | 32.6 | 2.9 | 238 | 1.0 | 52 | 18,6 | 2.8 | 6.5 | 1 | 0 |
| Queijo (cheddar) | 0,45 kg | 24.2 | 7.4 | 448 | 16.4 | 19 | 28.1 | 0,8 | 10.3 | 4 | 0 |
| Creme | 1/2 pt. | 14.1 | 3.5 | 49 | 1.7 | 3 | 16,9 | 0.6 | 2.5 | 0 | 17 |
| Manteiga de amendoim | 0,45 kg | 17,9 | 15.7 | 661 | 1.0 | 48 | 0 | 9.6 | 8.1 | 471 | 0 |
| Maionese | 1/2 pt. | 16.7 | 8.6 | 18 | 0,2 | 8 | 2.7 | 0.4 | 0.5 | 0 | 0 |
| Crisco | 0,45 kg | 20.3 | 20.1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Lardo | 0,45 kg | 9.8 | 41.7 | 0 | 0 | 0 | 0,2 | 0 | 0.5 | 5 | 0 |
| Filé de lombo | 0,45 kg | 39.6 | 2.9 | 166 | 0,1 | 34 | 0,2 | 2.1 | 2.9 | 69 | 0 |
| Bife redondo | 0,45 kg | 36.4 | 2.2 | 214 | 0,1 | 32 | 0.4 | 2.5 | 2.4 | 87 | 0 |
| Costela assada | 0,45 kg | 29.2 | 3.4 | 213 | 0,1 | 33 | 0 | 0 | 2 | 0 | 0 |
| Chuck assado | 0,45 kg | 22.6 | 3.6 | 309 | 0,2 | 46 | 0.4 | 1 | 4 | 120 | 0 |
| Prato | 0,45 kg | 14.6 | 8.5 | 404 | 0,2 | 62 | 0 | 0,9 | 0 | 0 | 0 |
| Fígado (carne) | 0,45 kg | 26.8 | 2.2 | 333 | 0,2 | 139 | 169.2 | 6.4 | 50,8 | 316 | 525 |
| Coxa de cordeiro | 0,45 kg | 27.6 | 3.1 | 245 | 0,1 | 20 | 0 | 2.8 | 3,9 | 86 | 0 |
| Costeletas de cordeiro (costela) | 0,45 kg | 36,6 | 3.3 | 140 | 0,1 | 15 | 0 | 1.7 | 2.7 | 54 | 0 |
| Costeletas de porco | 0,45 kg | 30,7 | 3.5 | 196 | 0,2 | 30 | 0 | 17.4 | 2.7 | 60 | 0 |
| Lombo de porco assado | 0,45 kg | 24.2 | 4.4 | 249 | 0.3 | 37 | 0 | 18.2 | 3.6 | 79 | 0 |
| Bacon | 0,45 kg | 25,6 | 10.4 | 152 | 0,2 | 23 | 0 | 1.8 | 1.8 | 71 | 0 |
| Presunto, defumado | 0,45 kg | 27.4 | 6.7 | 212 | 0,2 | 31 | 0 | 9.9 | 3.3 | 50 | 0 |
| Carne de porco salgada | 0,45 kg | 16 | 18,8 | 164 | 0,1 | 26 | 0 | 1.4 | 1.8 | 0 | 0 |
| Frango assado | 0,45 kg | 30.3 | 1.8 | 184 | 0,1 | 30 | 0,1 | 0,9 | 1.8 | 68 | 46 |
| Costeletas de vitela | 0,45 kg | 42.3 | 1.7 | 156 | 0,1 | 24 | 0 | 1.4 | 2.4 | 57 | 0 |
| Salmão, rosa (lata) | 450 g | 13 | 5.8 | 705 | 6.8 | 45 | 3.5 | 1 | 4.9 | 209 | 0 |
| Maçãs | 0,45 kg | 4.4 | 5.8 | 27 | 0.5 | 36 | 7.3 | 3.6 | 2.7 | 5 | 544 |
| Bananas | 0,45 kg | 6.1 | 4.9 | 60 | 0.4 | 30 | 17.4 | 2.5 | 3.5 | 28 | 498 |
| Limão | 1 doz. | 26 | 1.0 | 21 | 0.5 | 14 | 0 | 0.5 | 0 | 4 | 952 |
| Laranjas | 1 doz. | 30.9 | 2.2 | 40 | 1.1 | 18 | 11.1 | 3.6 | 1.3 | 10 | 1998 |
| Vagem | 0,45 kg | 7.1 | 2.4 | 138 | 3.7 | 80 | 69 | 4.3 | 5.8 | 37 | 862 |
| Repolho | 0,45 kg | 3.7 | 2.6 | 125 | 4,0 | 36 | 7.2 | 9 | 4.5 | 26 | 5369 |
| Cenouras | 1 monte | 4.7 | 2.7 | 73 | 2.8 | 43 | 188.5 | 6.1 | 4.3 | 89 | 608 |
| Aipo | 1 haste | 7.3 | 0,9 | 51 | 3.0 | 23 | 0,9 | 1.4 | 1.4 | 9 | 313 |
| Alface | 1 cabeça | 8.2 | 0.4 | 27 | 1.1 | 22 | 112.4 | 1.8 | 3.4 | 11 | 449 |
| Cebolas | 0,45 kg | 3.6 | 5.8 | 166 | 3,8 | 59 | 16.6 | 4.7 | 5.9 | 21 | 1184 |
| Batatas | 15 lb | 34 | 14.3 | 336 | 1.8 | 118 | 6.7 | 29.4 | 7.1 | 198 | 2522 |
| Espinafre | 0,45 kg | 8.1 | 1.1 | 106 | 0 | 138 | 918,4 | 5.7 | 13.8 | 33 | 2755 |
| Batatas-doce | 0,45 kg | 5.1 | 9.6 | 138 | 2.7 | 54 | 290.7 | 8.4 | 5.4 | 83 | 1912 |
| Pêssegos (lata) | No 2 1/2 | 16.8 | 3.7 | 20 | 0.4 | 10 | 21.5 | 0.5 | 1 | 31 | 196 |
| Peras (can) | No 2 1/2 | 20.4 | 3.0 | 8 | 0.3 | 8 | 0,8 | 0,8 | 0,8 | 5 | 81 |
| Abacaxi (lata) | No 2 1/2 | 21.3 | 2.4 | 16 | 0.4 | 8 | 2 | 2.8 | 0,8 | 7 | 399 |
| Aspargo (lata) | No 2 | 27,7 | 0.4 | 33 | 0.3 | 12 | 16.3 | 1.4 | 2.1 | 17 | 272 |
| Vagem (lata) | No 2 | 10 | 1.0 | 54 | 2 | 65 | 53.9 | 1.6 | 4.3 | 32 | 431 |
| Carne de porco e feijão (can) | 450 g | 7.1 | 7.5 | 364 | 4 | 134 | 3.5 | 8.3 | 7.7 | 56 | 0 |
| Milho (lata) | No 2 | 10.4 | 5.2 | 136 | 0,2 | 16 | 12 | 1.6 | 2.7 | 42 | 218 |
| Ervilha (lata) | No 2 | 13.8 | 2.3 | 136 | 0.6 | 45 | 34.9 | 4.9 | 2.5 | 37 | 370 |
| Tomates (lata) | No 2 | 8.6 | 1.3 | 63 | 0.7 | 38 | 53.2 | 3.4 | 2.5 | 36 | 1253 |
| Sopa de tomate (lata) | 300 mL | 7.6 | 1.6 | 71 | 0.6 | 43 | 57.9 | 3.5 | 2.4 | 67 | 862 |
| Pêssegos, secos | 0,45 kg | 15.7 | 8.5 | 87 | 1.7 | 173 | 86.8 | 1,2 | 4.3 | 55 | 57 |
| Ameixas secas | 0,45 kg | 9 | 12.8 | 99 | 2.5 | 154 | 85.7 | 3,9 | 4.3 | 65 | 257 |
| Passas secas | 450 g | 9.4 | 13.5 | 104 | 2.5 | 136 | 4.5 | 6.3 | 1.4 | 24 | 136 |
| Ervilhas desidratadas | 0,45 kg | 7,9 | 20.0 | 1367 | 4.2 | 345 | 2.9 | 28.7 | 18.4 | 162 | 0 |
| Feijão lima desidratado | 0,45 kg | 8.9 | 17.4 | 1055 | 3.7 | 459 | 5.1 | 26.9 | 38.2 | 93 | 0 |
| Feijão azul-marinho seco | 0,45 kg | 5.9 | 26.9 | 1691 | 11.4 | 792 | 0 | 38.4 | 24,6 | 217 | 0 |
| Café | 0,45 kg | 22,4 | 0 | 0 | 0 | 0 | 0 | 4 | 5.1 | 50 | 0 |
| Chá | 0,45 kg | 17.4 | 0 | 0 | 0 | 0 | 0 | 0 | 2.3 | 42 | 0 |
| Cacau | 226,8 g | 8.6 | 8.7 | 237 | 3 | 72 | 0 | 2 | 11.9 | 40 | 0 |
| Chocolate | 226,8 g | 16.2 | 8.0 | 77 | 1.3 | 39 | 0 | 0,9 | 3.4 | 14 | 0 |
| Açúcar | 10 lb | 51,7 | 34.9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Xarope de milho | 605 g | 13.7 | 14.7 | 0 | 0.5 | 74 | 0 | 0 | 0 | 5 | 0 |
| Melados | 450 g | 13.6 | 9.0 | 0 | 10.3 | 244 | 0 | 1.9 | 7.5 | 146 | 0 |
| Conservas de morango | 0,45 kg | 20.5 | 6.4 | 11 | 0.4 | 7 | 0,2 | 0,2 | 0.4 | 3 | 0 |
Como os nutrientes foram normalizados por preço, nosso objetivo é simplesmente minimizar a soma dos alimentos.
Em 1944, Stigler calculou a melhor resposta que poderia, observando com tristeza:
...parece que não há um método direto para encontrar o mínimo de uma função linear sujeito a condições lineares.
Ele encontrou uma dieta que custava US $39,93 por ano, em 1939. Em 1947, Jack Laderman usou o método simplex, que era uma invenção recente, para determinar a solução ideal. Levou 120 homens dias com nove funcionários em calculadoras de mesa para chegar à resposta.
Solução usando o solucionador linear
As seções a seguir apresentam um programa que resolve o problema da dieta Stigler.
Importar o wrapper do solucionador linear
Importe o wrapper de solucionador linear das ferramentas OR, uma interface para o solucionador linear [GLOP](/optimization/mip/glop0), conforme mostrado abaixo.
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;
Dados do problema
O código a seguir cria uma matriz nutrients para os
requisitos mínimos de nutrientes e uma
matriz data para a tabela de dados nutricionais
em qualquer solução.
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 })
};
Declarar o solucionador LP
O código a seguir instancia o wrapper MPsolver.
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;
}
Criar as variáveis
O código a seguir cria as variáveis para o problema.
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()}");
O método MakeNumVar cria uma variável, food[i], para cada linha da tabela.
Como mencionado anteriormente, os dados nutricionais são por dólar, então food[i] é a
quantidade de dinheiro para gastar em commodities i.
Definir as restrições
As restrições da dieta Stigler exigem que a quantidade total de nutrientes
fornecido por todos os alimentos seja pelo menos o requisito mínimo para cada nutriente.
Em seguida, escrevemos essas restrições como desigualdades envolvendo as matrizes data e nutrients, além das variáveis food[i].
Primeiro, a quantidade de nutriente i fornecida pelo alimento j por dólar é
data[j][i+3] (adicionamos três ao índice da coluna porque os dados nutricionais começam na
quarta coluna de data.) Como a quantidade de dinheiro a ser gasta nos alimentos j
é food[j], a quantidade de nutriente i fornecida pelo alimento j é
\(data[j][i+3] \cdot food[j]\).
Por fim, como o requisito mínimo para o nutriente i é nutrients[i][1], podemos programar a restrição i da seguinte maneira:
\(
\sum_{j} data[j][i+3] \cdot food[j] \geq nutrients[i][1] \;\;\;\;\; (1)
\)
O código a seguir define essas restrições.
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()}");
O método Constraint do Python (correspondente ao método C++
MakeRowConstraint
) cria as restrições para o problema. Para cada i,
constraint(nutrients[i][1], solver.infinity)
Isso cria uma restrição em que uma combinação linear das variáveis food[j] (definidas a seguir) é maior ou igual a nutrients[i][1].
Os coeficientes da expressão linear são definidos pelo método
SetCoefficient
da seguinte maneira: SetCoefficient(food[j], data[j][i+3]
Isso define o coeficiente de food[j] como data[j][i+3].
Juntando tudo isso, o código define as restrições expressas em (1) acima.
Crie o objetivo
O código a seguir define a função objetivo do problema.
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();
A função de objetivo é o custo total da comida, que é a soma das variáveis food[i].
O método
SetCoefficient
define os coeficientes da função de objetivo, que são todos 1 nesse caso.
Por fim, o
SetMinimization
declara que isso é um problema de minimização.
Invocar o solucionador
O código a seguir invoca o solucionador.
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();
O Glop resolve o problema de um computador comum em menos de 300 milissegundos:
Mostrar a solução
O código a seguir exibe a solução.
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})");
}
Este é o resultado do programa.
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
Código completo do programa
O código completo do programa de dieta Stigler é mostrado abaixo.
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");
}
}