Woofer Pet Foods Produces A Low 2

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?

Data:

Cost per pound
Vitamin 1 per pound
Vitamin 2 per pound
Beef
0.90
10 units
12 units
Grain
0.60 6 units 9 units

Model:

For this particular minimization problem the isocost line solution method is used.

a) Formulate this as an LP problem to minimize the cost of the dog food.

Minimize cost = $0.9X1 + $0.6X2 Subject to 10X1 + 6X2  9 12X1 + 9X2 10 X1, X2  0

b) How many pounds of beef and grain should be included in each pound of dog food?

Therefore, we find that the minimum cost of the dog food happens when
X1 = 0.9 and X2 = 0. The minimum cost is:

Cost (0.9,0) = $0.9  0.9 + $0.6  0 = $0.81

c) What is the cost and vitamin content of the final product?

Hence, 0.9 pounds of beef and no grain be included in each pound of dog food. Then the cost would be $0.81, the vitamin content would be

Vitamin 1 : 10X1 + 6X2 = 9
Vitamin 1 : 12X1 + 9X2 = 10.8