Economics > STUDY GUIDE > Georgia Institute Of Technology - ISYE 6501solution 15.2 (All)
Question 15.2 In the videos, we saw the “diet problem”. (The diet problem is one of the first large-scale optimization problems to be studied in practice. Back in the 1930’s and 40’s, the Ar... my wanted to meet the nutritional requirements of its soldiers while minimizing the cost.) In this homework you get to solve a diet problem with real data. The data is given in the file diet.xls. Here’s one possible solution. Please note that a good solution doesn’t have to try all of the possibilities in the code; they’re shown to help you learn, but they’re not necessary. 1. Formulate an optimization model (a linear program) to find the cheapest diet that satisfies the maximum and minimum daily nutrition constraints, and solve it using PuLP. Turn in your code and the solution. (The optimal solution should be a diet of air-popped popcorn, poached eggs, oranges, raw iceberg lettuce, raw celery, and frozen broccoli. UGH!) Algebraically, here’s what the model looks like: Data c j = cost per unit of food j a ij = amount of nutrient i per unit of food j m i = minimum amount of nutrient i required M i = maximum amount of nutrient i required Variables x j = amount of food j eaten Objective Minimize ∑ j c j x j (minimize total cost) Constraints ∑j a ij x j ≥ mi for each nutrient i (take in at least minimum amount of each nutrient) ∑j a ij x j ≤ Mi for each nutrient i (take in no more than max amount of each nutrient) x j ≥0 for each food j (can’t eat negative amounts) The file solution 15.2-1-separate.py shows one way to solve the problem. This file deals with each nutrient separately, to show what the problem looks like. However, an easier way to do it is shown in file solution 15.2-1-simpler.py, where data is read and constraints are written in a loop, so individual nutrients don’t need to each be written out. This will come in handy when there are more constraints (like the optional part below). However you set up the problem, here’s the optimal solution: ## ---------The solution to the diet problem is---------- ## 52.64371 units of Celery,_Raw This study source was downloaded by 100000793680026 from CourseHero.com on 04-04-2021 18:24:29 GMT -05:00 https://www.coursehero.com/file/50070049/solution-152docx/ This stud [Show More]
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