Question

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. (You don’t need to find the optimal solution to the model you formulate) ======== In your response please - define decision variables with NUN (Name, Unit, Notation) (e.g. Let E be the number of eggs in the meal) Then provide the mathematical model for the LP problem. - objective function - constraints

Answer 1

2x + 12y + 43 ≥ 40

17x + 12y + 8z ≥ 20

14x + 6y + z ≤ 50

x ≥ 0

y ≥ 0

z ≥ 0

Explanation:

given:

Cost Eggs = $2

Cost of edema = $5

cost of elbow Macaroni = $3

Lets eggs = x,

edamame = y

elbow macaroni = z

TC = 2x+5y+3z

Therefore;

2x + 12y + 43 ≥ 40

17x + 12y + 8z ≥ 20

14x + 6y + z ≤ 50

x ≥ 0

y ≥ 0

z ≥ 0

the first objective is to make sure the total cost is subject to the required nutritional requirements.

So the total cost function (TC) is denoted by the number of servings multiplied for each costs. Eggs cost $2, edamame $5, and macaroni $3.

The problem subjects that each meal contains at least 40g of carbohydrates (this is the condition).

to get this we need to add what each meal component adds to the total, eggs add 2g of carbs, edamame 12g, and macaroni 43g.

Same should be done for protein, we require at least 20 grams of protein, Eggs add 17g, edamame adds 12g, and macaroni adds 8g.

and lastly we don't want more than 50 grams of fat, Eggs add 14g, edamame add 6g and macaroni 1g.