Farmer Jane is trying to determine how to best feed her cows. She wants to make

Question

Farmer Jane is trying to determine how to best feed her cows. She wants to make sure each

cow is fed a daily diet that contains at least 240 grams (g) of fat, 360 g of carbohydrates, and 40 g of

protein. In addition, she wants to make sure that each cow's daily diet contains at most 30 g of sodium and

70 g of potassium. Farmer Jane has access to 3 different foods (Food X, Food Y, and Food Z) that she

can mix to create a blend for her cows. Food X contains 80 g of fat, 120 g of carbohydrates, 20 g of

protein, 10 g of sodium, and 30 g of potassium, and costs $2 per kilogram. Food Y contains 120 g of fat,

120 g of carbohydrates, 10 g of protein, 10 g of sodium, and 20 g of potassium, and costs $3 per kilogram.

Food Z contains 100 g of fat, 90 g of carbohydrates, 30 g of protein, 20 g of sodium, and 30 g of potassium,

and costs $2.4 per kilogram.

Write a linear program that determines a blend of Food X, Food Y, and Food Z that meets one cow's

nutritional requirements at minimum cost. Use the following decision variables:

X=kilograms of Food X in the blend,

Y= kilograms of Food Y in the blend,

Z= kilograms of Food Z in the blend.

Explanation / Answer

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