Question

The dietary director at a residential care facility can purchase ingredients to make two breakfast items, scrambled eggs and cheese or oatmeal for 40 cents and 30 cents per serving, respectively. Each serving of scrambled eggs contains 11 g of protein, 206 mg of cholesterol, and 0 grams of fiber. Each serving of oatmeal contains 6 g of protein, 0 mg of cholesterol, and 4 grams of fiber. To meet all the nutritional needs of the residents, there needs to be a minimum of 3500 grams of protein and maximum of 5000 grams. There should be a maximum of 9000 mg of cholesterol and a minimum of 1100 grams of fiber.

1. Write the Linear Program, in Excel and solve using Solver.

Answer 1

Let,

required serving of scrambled eggs = x1 and Oatmeal or cheese = x2

Objective is to minimize cost = Min 0.4x1+0.3x2

11x1+6x2 >= 3500(Min protein)
11x1+6x2 <= 5000(Max protein)
206x1+0*x2 <= 9000(cholesterol)
0*x1+4x2 >= 1100 (Fiber)

x1,x2 >= 0 (non-negativity constraint)

Solving in solver we get,
required serving of scrambled eggs = 43.68932039 and Oatmeal or cheese = 503.236246

Minimized cost = 168.4466019

Solver screenshot

Solver formula