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26 June, 10:03

You would like to make a nutritious meal of eggs, mixed vegetables and brown rice. The meal should provide at least 35 g of carbohydrates, at least 30 g of protein, and no more than 45 g of fat. One serving of eggs contains 2 g of carbohydrates, 18 g of protein, and 12 g of fat. A serving of mixed vegetables contains 14 g of carbohydrates, 15 g of protein, and 8 g of fat. A serving of rice contains 40 g of carbohydrates, 6 g of protein, and 1 g of fat. A serving of eggs costs $3.75, a serving of mixed vegetables costs $3.50, and a serving of rice costs $2. It is possible to order a partial serving, e. g. 0.75 servings of rice. Formulate a linear optimization model that could be used to determine the number of servings of eggs, mixed vegetables, and rice for your meal that meets the nutrition requirements at minimal cost.

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  1. 26 June, 11:43
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    Let G be the number of eggs in the meal

    V be the number of servings of mixed vegetables in the meal

    R be the number of servings of brown rice in the meal

    Objective function = Minimize 3.75G + 3.50V + 2R

    Constraints:

    2G + 14V + 40R ≥ 35 (Carbohydrates)

    18G + 15V + 6R ≥ 30 (Protein)

    12G + 8V + R ≤ 45 (Fat)

    G, M, B ≥ 0
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