331 lines
12 KiB
C++
331 lines
12 KiB
C++
// Copyright 2010-2025 Google LLC
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// [START program]
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// The Stigler diet problem.
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// [START import]
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#include <array>
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#include <cstddef>
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#include <cstdlib>
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#include <memory>
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#include <string>
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#include <utility> // std::pair
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#include <vector>
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#include "absl/base/log_severity.h"
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#include "absl/log/globals.h"
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#include "absl/log/log.h"
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#include "ortools/base/init_google.h"
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#include "ortools/linear_solver/linear_solver.h"
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// [END import]
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namespace operations_research {
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void StiglerDiet() {
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// [START data_model]
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// Nutrient minimums.
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const std::vector<std::pair<std::string, double>> nutrients = {
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{"Calories (kcal)", 3.0}, {"Protein (g)", 70.0},
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{"Calcium (g)", 0.8}, {"Iron (mg)", 12.0},
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{"Vitamin A (kIU)", 5.0}, {"Vitamin B1 (mg)", 1.8},
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{"Vitamin B2 (mg)", 2.7}, {"Niacin (mg)", 18.0},
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{"Vitamin C (mg)", 75.0}};
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struct Commodity {
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std::string name; //!< Commodity name
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std::string unit; //!< Unit
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double price; //!< 1939 price per unit (cents)
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//! Calories (kcal),
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//! Protein (g),
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//! Calcium (g),
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//! Iron (mg),
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//! Vitamin A (kIU),
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//! Vitamin B1 (mg),
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//! Vitamin B2 (mg),
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//! Niacin (mg),
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//! Vitamin C (mg)
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std::array<double, 9> nutrients;
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};
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std::vector<Commodity> data = {
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{"Wheat Flour (Enriched)",
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"10 lb.",
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36,
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{44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0}},
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{"Macaroni", "1 lb.", 14.1, {11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0}},
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{"Wheat Cereal (Enriched)",
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"28 oz.",
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24.2,
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{11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0}},
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{"Corn Flakes", "8 oz.", 7.1, {11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0}},
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{"Corn Meal",
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"1 lb.",
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4.6,
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{36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0}},
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{"Hominy Grits",
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"24 oz.",
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8.5,
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{28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0}},
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{"Rice", "1 lb.", 7.5, {21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0}},
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{"Rolled Oats", "1 lb.", 7.1, {25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0}},
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{"White Bread (Enriched)",
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"1 lb.",
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7.9,
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{15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0}},
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{"Whole Wheat Bread",
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"1 lb.",
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9.1,
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{12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0}},
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{"Rye Bread", "1 lb.", 9.1, {12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0}},
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{"Pound Cake", "1 lb.", 24.8, {8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0}},
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{"Soda Crackers", "1 lb.", 15.1, {12.5, 288, 0.5, 50, 0, 0, 0, 0, 0}},
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{"Milk", "1 qt.", 11, {6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177}},
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{"Evaporated Milk (can)",
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"14.5 oz.",
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6.7,
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{8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60}},
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{"Butter", "1 lb.", 30.8, {10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0}},
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{"Oleomargarine", "1 lb.", 16.1, {20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0}},
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{"Eggs", "1 doz.", 32.6, {2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0}},
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{"Cheese (Cheddar)",
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"1 lb.",
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24.2,
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{7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0}},
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{"Cream", "1/2 pt.", 14.1, {3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17}},
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{"Peanut Butter",
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"1 lb.",
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17.9,
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{15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0}},
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{"Mayonnaise", "1/2 pt.", 16.7, {8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0}},
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{"Crisco", "1 lb.", 20.3, {20.1, 0, 0, 0, 0, 0, 0, 0, 0}},
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{"Lard", "1 lb.", 9.8, {41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0}},
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{"Sirloin Steak",
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"1 lb.",
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39.6,
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{2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0}},
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{"Round Steak", "1 lb.", 36.4, {2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0}},
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{"Rib Roast", "1 lb.", 29.2, {3.4, 213, 0.1, 33, 0, 0, 2, 0, 0}},
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{"Chuck Roast", "1 lb.", 22.6, {3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0}},
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{"Plate", "1 lb.", 14.6, {8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0}},
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{"Liver (Beef)",
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"1 lb.",
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26.8,
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{2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525}},
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{"Leg of Lamb", "1 lb.", 27.6, {3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0}},
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{"Lamb Chops (Rib)",
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"1 lb.",
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36.6,
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{3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0}},
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{"Pork Chops", "1 lb.", 30.7, {3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0}},
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{"Pork Loin Roast",
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"1 lb.",
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24.2,
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{4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0}},
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{"Bacon", "1 lb.", 25.6, {10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0}},
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{"Ham, smoked", "1 lb.", 27.4, {6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0}},
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{"Salt Pork", "1 lb.", 16, {18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0}},
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{"Roasting Chicken",
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"1 lb.",
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30.3,
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{1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46}},
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{"Veal Cutlets", "1 lb.", 42.3, {1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0}},
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{"Salmon, Pink (can)",
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"16 oz.",
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13,
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{5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0}},
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{"Apples", "1 lb.", 4.4, {5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544}},
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{"Bananas", "1 lb.", 6.1, {4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498}},
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{"Lemons", "1 doz.", 26, {1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952}},
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{"Oranges", "1 doz.", 30.9, {2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998}},
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{"Green Beans", "1 lb.", 7.1, {2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862}},
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{"Cabbage", "1 lb.", 3.7, {2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369}},
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{"Carrots", "1 bunch", 4.7, {2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608}},
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{"Celery", "1 stalk", 7.3, {0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313}},
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{"Lettuce", "1 head", 8.2, {0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449}},
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{"Onions", "1 lb.", 3.6, {5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184}},
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{"Potatoes",
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"15 lb.",
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34,
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{14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522}},
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{"Spinach", "1 lb.", 8.1, {1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755}},
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{"Sweet Potatoes",
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"1 lb.",
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5.1,
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{9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912}},
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{"Peaches (can)",
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"No. 2 1/2",
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16.8,
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{3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196}},
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{"Pears (can)",
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"No. 2 1/2",
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20.4,
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{3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81}},
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{"Pineapple (can)",
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"No. 2 1/2",
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21.3,
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{2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399}},
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{"Asparagus (can)",
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"No. 2",
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27.7,
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{0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272}},
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{"Green Beans (can)",
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"No. 2",
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10,
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{1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431}},
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{"Pork and Beans (can)",
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"16 oz.",
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7.1,
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{7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0}},
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{"Corn (can)", "No. 2", 10.4, {5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218}},
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{"Peas (can)",
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"No. 2",
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13.8,
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{2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370}},
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{"Tomatoes (can)",
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"No. 2",
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8.6,
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{1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253}},
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{"Tomato Soup (can)",
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"10 1/2 oz.",
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7.6,
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{1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862}},
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{"Peaches, Dried",
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"1 lb.",
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15.7,
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{8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57}},
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{"Prunes, Dried",
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"1 lb.",
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9,
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{12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257}},
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{"Raisins, Dried",
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"15 oz.",
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9.4,
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{13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136}},
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{"Peas, Dried",
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"1 lb.",
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7.9,
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{20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0}},
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{"Lima Beans, Dried",
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"1 lb.",
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8.9,
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{17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0}},
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{"Navy Beans, Dried",
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"1 lb.",
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5.9,
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{26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0}},
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{"Coffee", "1 lb.", 22.4, {0, 0, 0, 0, 0, 4, 5.1, 50, 0}},
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{"Tea", "1/4 lb.", 17.4, {0, 0, 0, 0, 0, 0, 2.3, 42, 0}},
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{"Cocoa", "8 oz.", 8.6, {8.7, 237, 3, 72, 0, 2, 11.9, 40, 0}},
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{"Chocolate", "8 oz.", 16.2, {8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0}},
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{"Sugar", "10 lb.", 51.7, {34.9, 0, 0, 0, 0, 0, 0, 0, 0}},
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{"Corn Syrup", "24 oz.", 13.7, {14.7, 0, 0.5, 74, 0, 0, 0, 5, 0}},
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{"Molasses", "18 oz.", 13.6, {9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0}},
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{"Strawberry Preserves",
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"1 lb.",
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20.5,
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{6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0}}};
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// [END data_model]
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// [START solver]
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// Create the linear solver with the GLOP backend.
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std::unique_ptr<MPSolver> solver(MPSolver::CreateSolver("GLOP"));
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// [END solver]
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// [START variables]
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std::vector<MPVariable*> foods;
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const double infinity = solver->infinity();
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foods.reserve(data.size());
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for (const Commodity& commodity : data) {
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foods.push_back(solver->MakeNumVar(0.0, infinity, commodity.name));
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}
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LOG(INFO) << "Number of variables = " << solver->NumVariables();
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// [END variables]
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// [START constraints]
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// Create the constraints, one per nutrient.
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std::vector<MPConstraint*> constraints;
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for (std::size_t i = 0; i < nutrients.size(); ++i) {
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constraints.push_back(
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solver->MakeRowConstraint(nutrients[i].second, infinity));
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for (std::size_t j = 0; j < data.size(); ++j) {
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constraints.back()->SetCoefficient(foods[j], data[j].nutrients[i]);
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}
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}
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LOG(INFO) << "Number of constraints = " << solver->NumConstraints();
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// [END constraints]
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// [START objective]
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MPObjective* const objective = solver->MutableObjective();
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for (size_t i = 0; i < data.size(); ++i) {
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objective->SetCoefficient(foods[i], 1);
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}
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objective->SetMinimization();
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// [END objective]
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// [START solve]
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const MPSolver::ResultStatus result_status = solver->Solve();
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// [END solve]
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// [START print_solution]
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// Check that the problem has an optimal solution.
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if (result_status != MPSolver::OPTIMAL) {
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LOG(INFO) << "The problem does not have an optimal solution!";
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if (result_status == MPSolver::FEASIBLE) {
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LOG(INFO) << "A potentially suboptimal solution was found";
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} else {
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LOG(INFO) << "The solver could not solve the problem.";
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return;
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}
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}
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std::vector<double> nutrients_result(nutrients.size());
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LOG(INFO) << "";
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LOG(INFO) << "Annual Foods:";
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for (std::size_t i = 0; i < data.size(); ++i) {
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if (foods[i]->solution_value() > 0.0) {
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LOG(INFO) << data[i].name << ": $"
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<< std::to_string(365. * foods[i]->solution_value());
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for (std::size_t j = 0; j < nutrients.size(); ++j) {
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nutrients_result[j] +=
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data[i].nutrients[j] * foods[i]->solution_value();
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}
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}
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}
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LOG(INFO) << "";
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LOG(INFO) << "Optimal annual price: $"
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<< std::to_string(365. * objective->Value());
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LOG(INFO) << "";
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LOG(INFO) << "Nutrients per day:";
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for (std::size_t i = 0; i < nutrients.size(); ++i) {
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LOG(INFO) << nutrients[i].first << ": "
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<< std::to_string(nutrients_result[i]) << " (min "
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<< std::to_string(nutrients[i].second) << ")";
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}
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// [END print_solution]
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// [START advanced]
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LOG(INFO) << "";
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LOG(INFO) << "Advanced usage:";
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LOG(INFO) << "Problem solved in " << solver->wall_time() << " milliseconds";
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LOG(INFO) << "Problem solved in " << solver->iterations() << " iterations";
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// [END advanced]
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}
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} // namespace operations_research
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int main(int argc, char** argv) {
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InitGoogle(argv[0], &argc, &argv, true);
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absl::SetStderrThreshold(absl::LogSeverityAtLeast::kInfo);
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operations_research::StiglerDiet();
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return EXIT_SUCCESS;
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}
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// [END program]
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