A convalescent hospital wishes to provide, at a minimum cost, a diet that has a minimum of \(200 \mathrm{~g}\) of carbohydrates, \(100 \mathrm{~g}\) of protein, and \(20 \mathrm{~g}\) of fat per day. These requirements can be met with two foods, A and B:

If food A costs \(\$0.29\) per gram and food B costs \(\$ 0.15\) per gram, how many grams of each food should be purchased for each patient per day to meet the minimum requirements at the lowest cost?

Write a linear programming model, including the objective function and the set of constraints, for Problems 52-55. DO NOT SOLVE, but be sure to define all your variables.

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Food A B Carbohydrates 10 g 5 g Protein 2 g 5 g 5.0 Fats 3g 4 g