Linear Programming Models 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?
Please help!
Let X1 = the number of pounds of beef in each pound of dog food
X2 = the number of pounds of grain in each pound of dog food
Minimize.90X1+.60X2(minimize cost per pound of dog food)
Subject to:X1+X2=1(total weight should be one pound)
10X1+6X2≥9(at least 9 units of vitamin 1 in a pound)
12X1+9X2≥10(at least 10 units of vitamin 2 in a pound)
X1, X2≥0(non-negativity constraints)
Optimal Solution: X1 = .75 X2 = .25 Cost = $.825
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