1. An FBO (a "fixed-base-operator", usually the manager of a small-town airport) makes his revenue in three ways: flight instruction, charter flights, and aircraft maintenance. These activities earn revenues of $25/hour, $40/hour, and $35/hour respectively. The FBO has enough work to guarantee at least 40 hours of work per week. He also, for reasons of sanity and family, refuses to work more than 60 hours per week. He has at least ten hours of each activity to do each week, but refuses to more than twenty hours of any one of these activities to keep himself from getting bored with any one activity. How should he schedule his time to optimize his revenue?
2. A feed company produces a livestock mix from four possible ingredients: corn, peanuts, oats, and a vitamin supplement. The company produces the feed mix in 2,000 pound batches. Corn costs $0.10/lb, peanuts $0.05/lb, oats $0.15/lb, and the vitamin supplement $0.20/lb. Customers require the following criteria to be met:
- The mix must contain at least 30% peanuts.
- The mix cannot contain more than 20% oats.
- Each batch must contain at least 10% vitamin supplement.
- The ratio of corn and oats to peanuts must be at least 3 to 2.
What is the best batch mix that optimizes total cost?