Suppose the only foods in the world are as follows Price Limit FoodServing Energ

Question

Suppose the only foods in the world are as follows Price Limit FoodServing Energy Protein Calcium kcal 110 205 160 160 cents/serving) (Serving/da Size 28 g 100 g 2 Large 237 cc Oatmeal Chicken 24 12 54 285 32 13 13 Whole Milk Cherry Pie Pork & Beans 20 170g 420 260 g 260 14 80 19 After consulting with nutritionists, we decree that a satisfactory diet has at least 2000 kcal of energy, 55 g of protein, and 800 mg of calcium (vitamins and iron are supplied by pills). While some of us would be happy to subsist on 10 servings of pork and beans, we have decided to impose variety by having a limit on the number of servings/day for each of our six foods. Formulate this problem as an LP model. NO need to solve it.

Explanation / Answer

LP Model follows:

Let

X1 = number of servings of oatmeal to include in daily diet

X2 = number of servings of chicken to include in daily diet

X3 = number of servings of eggs to include in daily diet

X4 = number of servings of whole milk to include in daily diet

X5 = number of servings of cherry pie to include in daily diet

X6 = number of servings of pork & beans to include in daily diet

Objective: Min 3X1 + 24X2 + 13X3 + 9X4 + 20X5 + 19X6

s.t.

110X1 + 205X2 + 160X3 + 160X4 + 420X5 + 260X6 >= 2000

4X1 + 32X2 + 13X3 + 8X4 + 4X5 + 14X6 >= 55

2X1 + 24X2 + 13X3 + 9X4 + 20X5 + 19X6 >= 800

X1 <= 4

X2 <= 3

X3 <= 3

X4 <= 8

X5 <= 2

X6 <= 2

X1, X2, X3, X4, X5, X6 >= 0

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