Woofer Pet Foods produces a low-calorie dog food for overweight dogs. This produ

Question

Woofer Pet Foods produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.90, and each pound of grain costs $0.60. A pound of the dog food must contain at least 9 units of Vitamin 1 and 10 units of Vitamin 2. A pound of beef contains 10 units of Vitamin 1 and 12 units of Vitamin 2. A pound of grain contains 6 units of Vitamin 1 and 9 units of Vitamin 2. Formulate this as an LP problem to minimize the cost of the dog food. How many pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of the final product?

Explanation / Answer

Let x pounds be the beef required and y pounds be the grains required

Minimize Cost = 0.9x + 0.6y
subject to,
10x + 6y >= 9 .. Constraint of Vitamin 1
12x + 9y >= 10 .. Constraint of Vitamin 2

Solver Solution

Minimum cost is $0.81 for 1 pound.

Pounds of beef = 0.9

Pounds of grains = 0

Vitamin 1 content = 9 units

Vitamin 2 content = 10.8 units

Solver Solution x y Total Demand Decision Variables 0.9 0 Cost 0.9 0.6 0.81 Constraint 1 10 6 9 9 Constraint 2 12 9 10.8 10

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