Chapter 20, Problem 19SE

Warren Lloyd is interested in leasing a new car and has contacted three automobile dealers for pricing information. Each dealer offered Warren a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The monthly lease cost, the mileage allowance, and the cost for additional miles follow:

Warren decided to choose the lease option that will minimize his total 36-month cost. The difficulty is that Warren is not sure how many miles he will drive over the next three years. For purposes of this decision he believes it is reasonable to assume that he will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Warren estimated his total costs for the three lease options. For example, he figures that the Forno Automotive lease will cost him $10,764 if he drives 12,000 miles per year, $12,114 if he drives 15,000 miles per year, or $13,464 if he drives 18,000 miles per year.

1. a. What is the decision, and what is the chance event?
2. b. Construct a payoff table.
3. c. Suppose that the probabilities that Warren drives 12,000, 15,000, and 18,000 miles per year are 0.5, 0.4, and 0.1, respectively. What dealer should Warren choose?
4. d. Suppose that after further consideration, Warren concludes that the probabilities that he will drive 12,000, 15,000 and 18,000 miles per year are 0.3, 0.4, and 0.3, respectively. What dealer should Warren select?