Question 1. The dean of a college must plan the school's course offering for the fall semester. Student demands make it necessary to offer at least 30 undergraduate and 20 graduate courses in the term. Faculty contracts also dictate that at least 60 courses be offered in total. Each undergraduate course taught costs the college an average of $2500 in faculty wages and each graduate course costs $3000. How many undergraduate and graduate courses should be taught in the fall so that total faculty salaries are kept to a minimum?
Question 2 Pet food company produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $.90 cents, and each pound of grain costs $ .60 cents. 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?