এই বিভাগে, আমরা দেখিয়েছি কীভাবে স্টিগলার ডায়েট নামক একটি ক্লাসিক সমস্যার সমাধান করা যায়, যার নাম অর্থনীতিতে নোবেল বিজয়ী জর্জ স্টিগলারের নামে, যিনি খাদ্যের একটি সেট দিয়ে মৌলিক পুষ্টির চাহিদা পূরণের জন্য একটি সস্তা উপায় গণনা করেছিলেন। তিনি এটিকে একটি গাণিতিক অনুশীলন হিসাবে তুলে ধরেন, খাওয়ার সুপারিশ হিসাবে নয়, যদিও সর্বোত্তম পুষ্টি গণনা করার ধারণাটি সম্প্রতি প্রচলিত হয়েছে ।
স্টিগলার ডায়েট বাধ্যতামূলক করেছে যে এই ন্যূনতমগুলি পূরণ করা হবে:
পুষ্টি তালিকা
| পুষ্টি | দৈনিক প্রস্তাবিত গ্রহণ |
|---|---|
| ক্যালোরি | 3,000 ক্যালোরি |
| প্রোটিন | 70 গ্রাম |
| ক্যালসিয়াম | .8 গ্রাম |
| আয়রন | 12 মিলিগ্রাম |
| ভিটামিন এ | 5,000 আইইউ |
| থায়ামিন (ভিটামিন বি 1) | 1.8 মিলিগ্রাম |
| রিবোফ্লাভিন (ভিটামিন বি 2) | 2.7 মিলিগ্রাম |
| নিয়াসিন | 18 মিলিগ্রাম |
| অ্যাসকরবিক অ্যাসিড (ভিটামিন সি) | 75 মিলিগ্রাম |
স্টিগলারের মূল্যায়ন করা খাবারের সেটটি ছিল সেই সময়ের (1944) প্রতিফলন। নীচের পুষ্টির ডেটা প্রতি ডলার, প্রতি ইউনিট নয়, তাই উদ্দেশ্য হল প্রতিটি খাদ্যসামগ্রীর জন্য কত ডলার খরচ করতে হবে তা নির্ধারণ করা।
পণ্য তালিকা
| পণ্য | ইউনিট | 1939 মূল্য (সেন্ট) | ক্যালোরি (kcal) | প্রোটিন (ছ) | ক্যালসিয়াম (ছ) | আয়রন (মিগ্রা) | ভিটামিন এ (KIU) | থায়ামিন (মিগ্রা) | রিবোফ্লাভিন (মিগ্রা) | নিয়াসিন (মিগ্রা) | অ্যাসকরবিক অ্যাসিড (মিলিগ্রাম) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| গমের আটা (সমৃদ্ধ) | 10 পাউন্ড | 36 | 44.7 | 1411 | 2 | 365 | 0 | 55.4 | ৩৩.৩ | 441 | 0 |
| ম্যাকারনি | 1 পাউন্ড। | 14.1 | 11.6 | 418 | 0.7 | 54 | 0 | 3.2 | 1.9 | 68 | 0 |
| গমের সিরিয়াল (সমৃদ্ধ) | 28 oz | 24.2 | 11.8 | 377 | 14.4 | 175 | 0 | 14.4 | ৮.৮ | 114 | 0 |
| কর্ন ফ্লেক্স | 8 oz | 7.1 | 11.4 | 252 | 0.1 | 56 | 0 | 13.5 | 2.3 | 68 | 0 |
| ভুট্টা খাবার | 1 পাউন্ড। | 4.6 | 36.0 | 897 | 1.7 | 99 | 30.9 | 17.4 | ৭.৯ | 106 | 0 |
| হোমিনি গ্রিটস | 24 oz | 8.5 | 28.6 | 680 | 0.8 | 80 | 0 | 10.6 | 1.6 | 110 | 0 |
| ভাত | 1 পাউন্ড। | 7.5 | 21.2 | 460 | 0.6 | 41 | 0 | 2 | 4.8 | 60 | 0 |
| রোলড ওটস | 1 পাউন্ড। | 7.1 | 25.3 | 907 | 5.1 | 341 | 0 | 37.1 | ৮.৯ | 64 | 0 |
| সাদা রুটি (সমৃদ্ধ) | 1 পাউন্ড। | ৭.৯ | 15.0 | 488 | 2.5 | 115 | 0 | 13.8 | 8.5 | 126 | 0 |
| পুরো গমের রুটি | 1 পাউন্ড। | 9.1 | 12.2 | 484 | 2.7 | 125 | 0 | 13.9 | 6.4 | 160 | 0 |
| রাই রুটি | 1 পাউন্ড। | 9.1 | 12.4 | 439 | 1.1 | 82 | 0 | 9.9 | 3 | 66 | 0 |
| পাউন্ড কেক | 1 পাউন্ড। | 24.8 | ৮.০ | 130 | 0.4 | 31 | 18.9 | 2.8 | 3 | 17 | 0 |
| সোডা ক্র্যাকারস | 1 পাউন্ড। | 15.1 | 12.5 | 288 | 0.5 | 50 | 0 | 0 | 0 | 0 | 0 |
| দুধ | 1 কোয়া. | 11 | 6.1 | 310 | 10.5 | 18 | 16.8 | 4 | 16 | 7 | 177 |
| বাষ্পীভূত দুধ (ক্যান) | 14.5 oz | ৬.৭ | ৮.৪ | 422 | 15.1 | 9 | 26 | 3 | 23.5 | 11 | 60 |
| মাখন | 1 পাউন্ড। | 30.8 | 10.8 | 9 | 0.2 | 3 | 44.2 | 0 | 0.2 | 2 | 0 |
| ওলিওমার্জারিন | 1 পাউন্ড। | 16.1 | 20.6 | 17 | 0.6 | 6 | 55.8 | 0.2 | 0 | 0 | 0 |
| ডিম | 1 ডোজ। | 32.6 | 2.9 | 238 | 1.0 | 52 | 18.6 | 2.8 | 6.5 | 1 | 0 |
| পনির (চেডার) | 1 পাউন্ড। | 24.2 | 7.4 | 448 | 16.4 | 19 | 28.1 | 0.8 | 10.3 | 4 | 0 |
| ক্রিম | 1/2 pt. | 14.1 | 3.5 | 49 | 1.7 | 3 | 16.9 | 0.6 | 2.5 | 0 | 17 |
| পিনাট বাটার | 1 পাউন্ড। | 17.9 | 15.7 | 661 | 1.0 | 48 | 0 | 9.6 | 8.1 | 471 | 0 |
| মেয়োনিজ | 1/2 pt. | 16.7 | 8.6 | 18 | 0.2 | 8 | 2.7 | 0.4 | 0.5 | 0 | 0 |
| ক্রিসকো | 1 পাউন্ড। | 20.3 | 20.1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| লার্ড | 1 পাউন্ড। | ৯.৮ | 41.7 | 0 | 0 | 0 | 0.2 | 0 | 0.5 | 5 | 0 |
| সিরলোইন স্টেক | 1 পাউন্ড। | 39.6 | 2.9 | 166 | 0.1 | 34 | 0.2 | 2.1 | 2.9 | 69 | 0 |
| গোলাকার স্টেক | 1 পাউন্ড। | 36.4 | 2.2 | 214 | 0.1 | 32 | 0.4 | 2.5 | 2.4 | 87 | 0 |
| পাঁজর রোস্ট | 1 পাউন্ড। | 29.2 | 3.4 | 213 | 0.1 | 33 | 0 | 0 | 2 | 0 | 0 |
| চক রোস্ট | 1 পাউন্ড। | 22.6 | 3.6 | 309 | 0.2 | 46 | 0.4 | 1 | 4 | 120 | 0 |
| প্লেট | 1 পাউন্ড। | 14.6 | 8.5 | 404 | 0.2 | 62 | 0 | 0.9 | 0 | 0 | 0 |
| যকৃত (গরুর মাংস) | 1 পাউন্ড। | 26.8 | 2.2 | ৩৩৩ | 0.2 | 139 | 169.2 | 6.4 | 50.8 | 316 | 525 |
| লেগ অফ ল্যাম্ব | 1 পাউন্ড। | 27.6 | 3.1 | 245 | 0.1 | 20 | 0 | 2.8 | 3.9 | 86 | 0 |
| ল্যাম্ব চপস (পাঁজর) | 1 পাউন্ড। | 36.6 | 3.3 | 140 | 0.1 | 15 | 0 | 1.7 | 2.7 | 54 | 0 |
| শুয়োরের মাংস চপস | 1 পাউন্ড। | 30.7 | 3.5 | 196 | 0.2 | 30 | 0 | 17.4 | 2.7 | 60 | 0 |
| শুয়োরের মাংস কটি রোস্ট | 1 পাউন্ড। | 24.2 | 4.4 | 249 | 0.3 | 37 | 0 | 18.2 | 3.6 | 79 | 0 |
| বেকন | 1 পাউন্ড। | 25.6 | 10.4 | 152 | 0.2 | 23 | 0 | 1.8 | 1.8 | 71 | 0 |
| হ্যাম, ধূমপান | 1 পাউন্ড। | 27.4 | ৬.৭ | 212 | 0.2 | 31 | 0 | 9.9 | 3.3 | 50 | 0 |
| লবণ শুয়োরের মাংস | 1 পাউন্ড। | 16 | 18.8 | 164 | 0.1 | 26 | 0 | 1.4 | 1.8 | 0 | 0 |
| রোস্টিং চিকেন | 1 পাউন্ড। | 30.3 | 1.8 | 184 | 0.1 | 30 | 0.1 | 0.9 | 1.8 | 68 | 46 |
| ভেল কাটলেট | 1 পাউন্ড। | 42.3 | 1.7 | 156 | 0.1 | 24 | 0 | 1.4 | 2.4 | 57 | 0 |
| সালমন, গোলাপী (পান) | 16 oz | 13 | ৫.৮ | 705 | ৬.৮ | 45 | 3.5 | 1 | 4.9 | 209 | 0 |
| আপেল | 1 পাউন্ড। | 4.4 | ৫.৮ | 27 | 0.5 | 36 | 7.3 | 3.6 | 2.7 | 5 | 544 |
| কলা | 1 পাউন্ড। | 6.1 | 4.9 | 60 | 0.4 | 30 | 17.4 | 2.5 | 3.5 | 28 | 498 |
| লেবু | 1 ডোজ। | 26 | 1.0 | 21 | 0.5 | 14 | 0 | 0.5 | 0 | 4 | 952 |
| কমলালেবু | 1 ডোজ। | 30.9 | 2.2 | 40 | 1.1 | 18 | 11.1 | 3.6 | 1.3 | 10 | 1998 |
| সবুজ মটরশুটি | 1 পাউন্ড। | 7.1 | 2.4 | 138 | 3.7 | 80 | 69 | 4.3 | ৫.৮ | 37 | 862 |
| বাঁধাকপি | 1 পাউন্ড। | 3.7 | 2.6 | 125 | 4.0 | 36 | 7.2 | 9 | 4.5 | 26 | 5369 |
| গাজর | 1 গুচ্ছ | 4.7 | 2.7 | 73 | 2.8 | 43 | 188.5 | 6.1 | 4.3 | ৮৯ | 608 |
| সেলারি | 1 ডালপালা | 7.3 | 0.9 | 51 | 3.0 | 23 | 0.9 | 1.4 | 1.4 | 9 | 313 |
| লেটুস | 1 মাথা | 8.2 | 0.4 | 27 | 1.1 | 22 | 112.4 | 1.8 | 3.4 | 11 | 449 |
| পেঁয়াজ | 1 পাউন্ড। | 3.6 | ৫.৮ | 166 | 3.8 | 59 | 16.6 | 4.7 | ৫.৯ | 21 | 1184 |
| আলু | 15 পাউন্ড | 34 | 14.3 | 336 | 1.8 | 118 | ৬.৭ | 29.4 | 7.1 | 198 | 2522 |
| পালং শাক | 1 পাউন্ড। | 8.1 | 1.1 | 106 | 0 | 138 | 918.4 | ৫.৭ | 13.8 | 33 | 2755 |
| মিষ্টি আলু | 1 পাউন্ড। | 5.1 | 9.6 | 138 | 2.7 | 54 | 290.7 | ৮.৪ | 5.4 | 83 | 1912 |
| পীচ (পারি) | নং 2 1/2 | 16.8 | 3.7 | 20 | 0.4 | 10 | 21.5 | 0.5 | 1 | 31 | 196 |
| নাশপাতি (পারি) | নং 2 1/2 | 20.4 | 3.0 | 8 | 0.3 | 8 | 0.8 | 0.8 | 0.8 | 5 | 81 |
| আনারস (পান) | নং 2 1/2 | 21.3 | 2.4 | 16 | 0.4 | 8 | 2 | 2.8 | 0.8 | 7 | 399 |
| অ্যাসপারাগাস (পারি) | নং 2 | 27.7 | 0.4 | 33 | 0.3 | 12 | 16.3 | 1.4 | 2.1 | 17 | 272 |
| সবুজ মটরশুটি (পান) | নং 2 | 10 | 1.0 | 54 | 2 | 65 | 53.9 | 1.6 | 4.3 | 32 | 431 |
| শুকরের মাংস এবং মটরশুটি (পারি) | 16 oz | 7.1 | 7.5 | 364 | 4 | 134 | 3.5 | 8.3 | 7.7 | 56 | 0 |
| ভুট্টা (পান) | নং 2 | 10.4 | 5.2 | 136 | 0.2 | 16 | 12 | 1.6 | 2.7 | 42 | 218 |
| মটর (পান) | নং 2 | 13.8 | 2.3 | 136 | 0.6 | 45 | 34.9 | 4.9 | 2.5 | 37 | 370 |
| টমেটো (পান) | নং 2 | 8.6 | 1.3 | 63 | 0.7 | 38 | 53.2 | 3.4 | 2.5 | 36 | 1253 |
| টমেটো স্যুপ (পান) | 10 1/2 oz | 7.6 | 1.6 | 71 | 0.6 | 43 | 57.9 | 3.5 | 2.4 | 67 | 862 |
| পীচ, শুকনো | 1 পাউন্ড। | 15.7 | 8.5 | 87 | 1.7 | 173 | ৮৬.৮ | 1.2 | 4.3 | 55 | 57 |
| ছাঁটাই, শুকনো | 1 পাউন্ড। | 9 | 12.8 | 99 | 2.5 | 154 | ৮৫.৭ | 3.9 | 4.3 | 65 | 257 |
| কিশমিশ, শুকনো | 15 oz | 9.4 | 13.5 | 104 | 2.5 | 136 | 4.5 | 6.3 | 1.4 | 24 | 136 |
| মটর, শুকনো | 1 পাউন্ড। | ৭.৯ | 20.0 | 1367 | 4.2 | 345 | 2.9 | 28.7 | 18.4 | 162 | 0 |
| লিমা মটরশুটি, শুকনো | 1 পাউন্ড। | ৮.৯ | 17.4 | 1055 | 3.7 | 459 | 5.1 | 26.9 | 38.2 | 93 | 0 |
| নেভি মটরশুটি, শুকনো | 1 পাউন্ড। | ৫.৯ | 26.9 | 1691 | 11.4 | 792 | 0 | 38.4 | 24.6 | 217 | 0 |
| কফি | 1 পাউন্ড। | 22.4 | 0 | 0 | 0 | 0 | 0 | 4 | 5.1 | 50 | 0 |
| চা | 1/4 পাউন্ড | 17.4 | 0 | 0 | 0 | 0 | 0 | 0 | 2.3 | 42 | 0 |
| কোকো | 8 oz | 8.6 | ৮.৭ | 237 | 3 | 72 | 0 | 2 | 11.9 | 40 | 0 |
| চকোলেট | 8 oz | 16.2 | ৮.০ | 77 | 1.3 | 39 | 0 | 0.9 | 3.4 | 14 | 0 |
| চিনি | 10 পাউন্ড | 51.7 | 34.9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| কর্ন সিরাপ | 24 oz | 13.7 | 14.7 | 0 | 0.5 | 74 | 0 | 0 | 0 | 5 | 0 |
| গুড় | 18 oz | 13.6 | 9.0 | 0 | 10.3 | 244 | 0 | 1.9 | 7.5 | 146 | 0 |
| স্ট্রবেরি সংরক্ষণ করে | 1 পাউন্ড। | 20.5 | 6.4 | 11 | 0.4 | 7 | 0.2 | 0.2 | 0.4 | 3 | 0 |
যেহেতু পুষ্টি উপাদানগুলি মূল্য দ্বারা স্বাভাবিক করা হয়েছে, তাই আমাদের উদ্দেশ্য কেবলমাত্র খাবারের যোগফলকে হ্রাস করা।
1944 সালে, স্টিগলার দুঃখের সাথে উল্লেখ করে তার পক্ষে সবচেয়ে ভাল উত্তর গণনা করেছিলেন:
...রৈখিক অবস্থার সাপেক্ষে ন্যূনতম লিনিয়ার ফাংশন খুঁজে বের করার কোনো সরাসরি পদ্ধতি আছে বলে মনে হয় না।
1939 ডলারে তিনি একটি খাদ্য খুঁজে পান যার খরচ প্রতি বছর $39.93। 1947 সালে, জ্যাক লেডারম্যান সর্বোত্তম সমাধান নির্ধারণের জন্য সিমপ্লেক্স পদ্ধতি (তখন, একটি সাম্প্রতিক উদ্ভাবন!) ব্যবহার করেছিলেন। উত্তরে পৌঁছতে ডেস্ক ক্যালকুলেটরে নয়জন কেরানির 120 জন দিন লেগেছে।
লিনিয়ার সলভার ব্যবহার করে সমাধান
নিম্নলিখিত বিভাগগুলি একটি প্রোগ্রাম উপস্থাপন করে যা স্টিগলার ডায়েট সমস্যার সমাধান করে।
রৈখিক সমাধানকারী মোড়ক আমদানি করুন
OR-Tools লিনিয়ার সলভার র্যাপার আমদানি করুন, [GLOP](/optimization/mip/glop0 লিনিয়ার সলভারের জন্য একটি ইন্টারফেস, নীচে দেখানো হয়েছে।
পাইথন
from ortools.linear_solver import pywraplp
সি++
#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"
জাভা
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;
সি#
using System; using System.Collections.Generic; using Google.OrTools.LinearSolver;
সমস্যার জন্য ডেটা
নিম্নলিখিত কোডটি ন্যূনতম পুষ্টির প্রয়োজনীয়তার জন্য একটি অ্যারে nutrients তৈরি করে এবং যে কোনও সমাধানে পুষ্টির ডেটা টেবিলের জন্য একটি অ্যারে data তৈরি করে।
পাইথন
# 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 ]
সি++
// 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}}};
জাভা
// 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}});
সি#
// 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 }) };
এলপি সলভার ঘোষণা করুন
নিম্নলিখিত কোডটি MPsolver র্যাপারকে ইনস্ট্যান্টিয়েট করে।
পাইথন
# Instantiate a Glop solver and naming it. solver = pywraplp.Solver.CreateSolver("GLOP") if not solver: return
সি++
// Create the linear solver with the GLOP backend. std::unique_ptr<MPSolver> solver(MPSolver::CreateSolver("GLOP"));
জাভা
// 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; }
সি#
// Create the linear solver with the GLOP backend. Solver solver = Solver.CreateSolver("GLOP"); if (solver is null) { return; }
ভেরিয়েবল তৈরি করুন
নিম্নলিখিত কোডটি সমস্যার জন্য ভেরিয়েবল তৈরি করে।
পাইথন
# 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())
সি++
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();
জাভা
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());
সি#
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 পদ্ধতিটি টেবিলের প্রতিটি সারির জন্য একটি পরিবর্তনশীল, food[i] তৈরি করে। পূর্বে উল্লিখিত হিসাবে, পুষ্টির তথ্য প্রতি ডলার, তাই food[i] হল পণ্যের জন্য ব্যয় করা অর্থের পরিমাণ i
সীমাবদ্ধতা সংজ্ঞায়িত করুন
স্টিগলারের খাদ্যের সীমাবদ্ধতার জন্য সমস্ত খাবারের দ্বারা সরবরাহ করা পুষ্টির মোট পরিমাণ প্রতিটি পুষ্টির জন্য কমপক্ষে ন্যূনতম প্রয়োজন। এর পরে, আমরা এই সীমাবদ্ধতাগুলিকে অ্যারে data এবং nutrients এবং ভেরিয়েবল food[i] জড়িত অসমতা হিসাবে লিখি।
প্রথমত, প্রতি ডলারে খাদ্য j দ্বারা i পুষ্টির পরিমাণ হল data[j][i+3] (আমরা কলাম সূচকে 3 যোগ করি কারণ পুষ্টির ডেটা data চতুর্থ কলামে শুরু হয়।) যেহেতু অর্থের পরিমাণ খাবারের j i করা হয় j হল food[j]\(data[j][i+3] \cdot food[j]\). পরিশেষে, যেহেতু পুষ্টি i এর জন্য ন্যূনতম প্রয়োজনীয়তা হল nutrients[i][1] , আমরা নিম্নরূপ সীমাবদ্ধতা i লিখতে পারি:
\(
\sum_{j} data[j][i+3] \cdot food[j] \geq nutrients[i][1] \;\;\;\;\; (1)
\)
নিম্নলিখিত কোড এই সীমাবদ্ধতা সংজ্ঞায়িত করে। পাইথন
# 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())
সি++
// 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();
জাভা
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());
সি#
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()}");
পাইথন পদ্ধতির Constraint (C++ পদ্ধতি MakeRowConstraint এর সাথে সম্পর্কিত) সমস্যার জন্য সীমাবদ্ধতা তৈরি করে। প্রতিটি i জন্য, constraint(nutrients[i][1], solver.infinity)
এটি একটি সীমাবদ্ধতা তৈরি করে যেখানে food[j] (পরবর্তীতে সংজ্ঞায়িত) nutrients[i][1] । লিনিয়ার এক্সপ্রেশনের সহগগুলি SetCoefficient পদ্ধতি দ্বারা নিম্নরূপ সংজ্ঞায়িত করা হয়েছে: SetCoefficient(food[j], data[j][i+3]
এটি food[j] সহগকে data[j][i+3] হিসাবে সেট করে।
এই সব একসাথে রেখে, কোডটি উপরের (1) এ প্রকাশিত সীমাবদ্ধতাগুলিকে সংজ্ঞায়িত করে।
উদ্দেশ্য তৈরি করুন
নিম্নলিখিত কোড সমস্যার জন্য উদ্দেশ্য ফাংশন সংজ্ঞায়িত করে।
পাইথন
# Objective function: Minimize the sum of (price-normalized) foods. objective = solver.Objective() for food in foods: objective.SetCoefficient(food, 1) objective.SetMinimization()
সি++
MPObjective* const objective = solver->MutableObjective(); for (size_t i = 0; i < data.size(); ++i) { objective->SetCoefficient(foods[i], 1); } objective->SetMinimization();
জাভা
MPObjective objective = solver.objective(); for (int i = 0; i < data.size(); ++i) { objective.setCoefficient(foods.get(i), 1); } objective.setMinimization();
সি#
Objective objective = solver.Objective(); for (int i = 0; i < data.Length; ++i) { objective.SetCoefficient(foods[i], 1); } objective.SetMinimization();
উদ্দেশ্য ফাংশন হল খাদ্যের মোট খরচ, যা food[i] ।
SetCoefficient পদ্ধতিটি উদ্দেশ্যমূলক ফাংশনের সহগ নির্ধারণ করে, যা এই ক্ষেত্রে 1 । অবশেষে, SetMinimization এটিকে একটি মিনিমাইজেশন সমস্যা বলে ঘোষণা করে।
সমাধানকারীকে আহ্বান করুন
নিম্নলিখিত কোডটি সমাধানকারীকে আহ্বান করে।
পাইথন
print(f"Solving with {solver.SolverVersion()}")
status = solver.Solve()সি++
const MPSolver::ResultStatus result_status = solver->Solve();
জাভা
final MPSolver.ResultStatus resultStatus = solver.solve();
সি#
Solver.ResultStatus resultStatus = solver.Solve();
Glop একটি সাধারণ কম্পিউটারে 300 মিলিসেকেন্ডের কম সময়ে সমস্যা সমাধান করে:
সমাধান প্রদর্শন করুন
নিম্নলিখিত কোড সমাধান প্রদর্শন করে.
পাইথন
# 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]) )
সি++
// 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) << ")"; }
জাভা
// 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: $" + 365 * objective.value()); System.out.println("\nNutrients per day:"); for (int i = 0; i < nutrients.size(); ++i) { System.out.println( nutrients.get(i)[0] + ": " + nutrientsResult[i] + " (min " + nutrients.get(i)[1] + ")"); }
সি#
// Check that the problem has an optimal solution. if (resultStatus != Solver.ResultStatus.OPTIMAL) { Console.WriteLine("The problem does not have an optimal solution!"); if (resultStatus == Solver.ResultStatus.FEASIBLE) { Console.WriteLine("A potentially suboptimal solution was found."); } else { Console.WriteLine("The solver could not solve the problem."); return; } } // Display the amounts (in dollars) to purchase of each food. double[] nutrientsResult = new double[nutrients.Length]; Console.WriteLine("\nAnnual Foods:"); for (int i = 0; i < foods.Count; ++i) { if (foods[i].SolutionValue() > 0.0) { Console.WriteLine($"{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})"); }
এখানে প্রোগ্রামের আউটপুট আছে।
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
প্রোগ্রামের জন্য সম্পূর্ণ কোড
Stigler ডায়েট প্রোগ্রামের সম্পূর্ণ কোড নীচে দেখানো হয়েছে।
পাইথন
"""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()
সি++
// 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; }
জাভা
// 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() {} }
সি#
// 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"); } }