Woofer Pet Foods produces a low-calorie dog food for overweight dogs. This productis made from beef products and grain. Each pound of beef costs $1.50, and each pound of graincosts $0.70. A pound of the dog food must contain at least 9 units of Vitamin 1, 10 units ofVitamin 2, and 6 units of Vitamin 3. A pound of beef contains 6 units of Vitamin 1, 12 units ofVitamin 2, and 4 units of Vitamin 3. A pound of grain contains 12 units of Vitamin 1, 9 units ofVitamin 2, and 10 units of Vitamin 3. Formulate this as a LP problem to minimize the cost of thedog food.
a. How many pounds of beef and grain should be included in each pound of dog food?
b. What is the cost and vitamin content of the final product?
c. What would the distribution of beef and grain be if the cost of beef increased to $3.50 per pound?