292 lines
11 KiB
Python
Executable File
292 lines
11 KiB
Python
Executable File
#!/usr/bin/env python3
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# Copyright 2010-2022 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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A description of the problem can be found here:
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https://en.wikipedia.org/wiki/Stigler_diet.
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"""
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# [START import]
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from ortools.linear_solver import pywraplp
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# [END import]
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def main():
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"""Entry point of the program."""
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# Instantiate the data problem.
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# [START data_model]
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# Nutrient minimums.
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nutrients = [
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["Calories (kcal)", 3],
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["Protein (g)", 70],
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["Calcium (g)", 0.8],
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["Iron (mg)", 12],
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["Vitamin A (KIU)", 5],
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["Vitamin B1 (mg)", 1.8],
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["Vitamin B2 (mg)", 2.7],
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["Niacin (mg)", 18],
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["Vitamin C (mg)", 75],
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]
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# Commodity, Unit, 1939 price (cents), Calories (kcal), Protein (g),
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# Calcium (g), Iron (mg), Vitamin A (KIU), Vitamin B1 (mg), Vitamin B2 (mg),
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# Niacin (mg), Vitamin C (mg)
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data = [
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[
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"Wheat Flour (Enriched)",
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"10 lb.",
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36,
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44.7,
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1411,
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2,
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365,
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0,
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55.4,
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33.3,
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441,
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0,
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],
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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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[
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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,
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377,
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14.4,
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175,
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0,
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14.4,
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8.8,
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114,
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0,
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],
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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", "1 lb.", 4.6, 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0],
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["Hominy Grits", "24 oz.", 8.5, 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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[
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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,
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488,
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2.5,
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115,
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0,
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13.8,
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8.5,
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126,
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0,
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],
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["Whole Wheat Bread", "1 lb.", 9.1, 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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[
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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,
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422,
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15.1,
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9,
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26,
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3,
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23.5,
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11,
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60,
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],
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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)", "1 lb.", 24.2, 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", "1 lb.", 17.9, 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", "1 lb.", 39.6, 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)", "1 lb.", 26.8, 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)", "1 lb.", 36.6, 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", "1 lb.", 24.2, 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", "1 lb.", 30.3, 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)", "16 oz.", 13, 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", "15 lb.", 34, 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", "1 lb.", 5.1, 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912],
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["Peaches (can)", "No. 2 1/2", 16.8, 3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196],
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["Pears (can)", "No. 2 1/2", 20.4, 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81],
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["Pineapple (can)", "No. 2 1/2", 21.3, 2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399],
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["Asparagus (can)", "No. 2", 27.7, 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272],
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["Green Beans (can)", "No. 2", 10, 1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431],
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["Pork and Beans (can)", "16 oz.", 7.1, 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)", "No. 2", 13.8, 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370],
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["Tomatoes (can)", "No. 2", 8.6, 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253],
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[
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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,
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71,
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0.6,
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43,
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57.9,
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3.5,
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2.4,
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67,
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862,
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],
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["Peaches, Dried", "1 lb.", 15.7, 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57],
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["Prunes, Dried", "1 lb.", 9, 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257],
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["Raisins, Dried", "15 oz.", 9.4, 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136],
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["Peas, Dried", "1 lb.", 7.9, 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0],
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[
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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,
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1055,
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3.7,
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459,
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5.1,
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26.9,
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38.2,
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93,
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0,
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],
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[
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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,
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1691,
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11.4,
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792,
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0,
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38.4,
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24.6,
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217,
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0,
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],
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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", "1 lb.", 20.5, 6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0],
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]
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# [END data_model]
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# [START solver]
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# Instantiate a Glop solver and naming it.
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solver = pywraplp.Solver.CreateSolver("GLOP")
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if not solver:
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return
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# [END solver]
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# [START variables]
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# Declare an array to hold our variables.
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foods = [solver.NumVar(0.0, solver.infinity(), item[0]) for item in data]
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print("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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constraints = []
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for i, nutrient in enumerate(nutrients):
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constraints.append(solver.Constraint(nutrient[1], solver.infinity()))
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for j, item in enumerate(data):
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constraints[i].SetCoefficient(foods[j], item[i + 3])
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print("Number of constraints =", solver.NumConstraints())
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# [END constraints]
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# [START objective]
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# Objective function: Minimize the sum of (price-normalized) foods.
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objective = solver.Objective()
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for food in foods:
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objective.SetCoefficient(food, 1)
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objective.SetMinimization()
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# [END objective]
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# [START solve]
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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 status != solver.OPTIMAL:
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print("The problem does not have an optimal solution!")
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if status == solver.FEASIBLE:
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print("A potentially suboptimal solution was found.")
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else:
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print("The solver could not solve the problem.")
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exit(1)
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# Display the amounts (in dollars) to purchase of each food.
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nutrients_result = [0] * len(nutrients)
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print("\nAnnual Foods:")
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for i, food in enumerate(foods):
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if food.solution_value() > 0.0:
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print("{}: ${}".format(data[i][0], 365.0 * food.solution_value()))
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for j, _ in enumerate(nutrients):
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nutrients_result[j] += data[i][j + 3] * food.solution_value()
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print("\nOptimal annual price: ${:.4f}".format(365.0 * objective.Value()))
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print("\nNutrients per day:")
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for i, nutrient in enumerate(nutrients):
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print(
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"{}: {:.2f} (min {})".format(nutrient[0], nutrients_result[i], nutrient[1])
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)
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# [END print_solution]
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# [START advanced]
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print("\nAdvanced usage:")
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print("Problem solved in ", solver.wall_time(), " milliseconds")
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print("Problem solved in ", solver.iterations(), " iterations")
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# [END advanced]
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if __name__ == "__main__":
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main()
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# [END program]
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