Question

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.

Answer 1

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