Problem:
Amy Lloyd is interested in leasing a new Saab and has contacted three automobile dealers for pricing information. Each dealer offered Amy 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
|
Dealer
|
Monthly Cost
|
Mileage Allowance
|
Cost per Additional Mile
|
|
Forno Saab
|
$299
|
36,000
|
$0.15
|
|
Midtown Motors
|
$310
|
45,000
|
$0.20
|
|
Hopkins Automotive
|
$325
|
54,000
|
$0.15
|
Amy decided to choose the lease option that will minimize her total 36-month cost. The difficulty is that Amy is not sure how many miles she will drive over the next three years. For purposes of the decision she believes it is reasonable to assume that she will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Amy estimated her total cost for the three lease options. For example, she figures that the Forno Saab lease will cost her $10,764 if she drives 12,000 miles per year, $12,114 if she drives 15,000 miles per year, or $13,464 if she drives 18,000 miles per year.
a. Construct a complete payoff table for Amy's decision.
b. If Amy is uncertain as to which of the three mileage assumptions is most appropriate, determine the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches.
c. Suppose that the probabilities that Amy drives 12,000, 15,000 and 18,000 miles per year are 0.5, 0.4, and 0.1, respectively. Determine the action Amy should choose using the expected value approach.
d. Suppose that after further consideration, Amy concludes that the probabilities that she will drive 12,000, 15,000, and 18,000 miles per year are 0.3, 0.4, and 0.3, respectively. Determine the action Amy should choose using the expected value approach.