question archive You would like to make a nutritious meal of eggs, edamame, and elbow macaroni
You would like to make a nutritious meal of eggs, edamame, and elbow macaroni
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You would like to make a nutritious meal of eggs, edamame, and elbow macaroni.
The meal should provide at least 40 g of carbohydrates, at least 20 g of protein, and no more than 50 g of fat. An egg
(one serving) contains 2 g of carbohydrates, 17 g of protein, and 14 g of fat. A serving of edamame contains 12 g of carbohydrates, 12 g of protein, and 6 g of fat. A serving of elbow macaroni contains 43 g of carbohydrates, 8 g of protein, and 1 g of fat.
An egg costs $2, a serving of edamame costs $ 5, and a serving of elbow macaroni costs $3.
Formulate a linear optimization model that could be used to determine the number of servings of egg, edamame, and elbow macaroni that should be in the meal in order to meet the nutrition requirements at minimal cost.
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First we represent the problem in tabular form: Carbohydrates Protein Fat Egg 2g 17g 14g edamame 12g 12g 6g elbow macaroni 43g 8g 1g Total >=40g >=20g <=50 Given: An egg costs $2, a serving of edamame costs $5, and a serving of elbow macaroni contains 43 g of carbohydrates, 8 g of protein, and 1 g of fat.
Step-by-step explanation
Solution
Let number of eggs be X
Let number of edamame be Y
Let number of elbow macaroni be X
2X + 12Y + 43Z ≥ 40
17X + 12Y + 8Z ≥ 20
14X + 6Y + Z ≤ 50
Objective function
Minimize the cost = (2X + 5Y + 3Z)
