Amy Lloyd is interested in leasing a new Honda 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 Hepburn Honda $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 this 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 costs for the three lease options. For example, she figures that the Hepburn Honda lease will cost her 36($299) + $0.15(36,000 - 36,000) = $10,764 if she drives 12,000 miles per year, 36($299) + $0.15(45,000 - 36,000) = $12,114 if she drives 15,000 miles per year, or 36($299) + $0.15(54,000 - 36,000) = $13,464 if she drives 18,000 miles per year. (a) What is the decision, and what is the chance event? Choose the correct answer below. (i) The decision is to select the number of miles Amy will drive and the chance event is the three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive). (ii) The decision is to select the monthly cost and the chance event is the three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive). (iii) The decision is to select the best lease option from three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive) and the chance event is the number of miles Amy will drive. (iv) The decision is to select the best lease option from three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive) and the chance event is the monthly cost that Amy will incur. (b) Construct a payoff table for Amy's problem. Actual Miles Driven Annually Dealer 12,000 15,000 18,000 Hepburn Honda $ $ $ Midtown Motors $ $ $ Hopkins Automotive $ $ $ (c) If Amy has no idea which of the three mileage assumptions is most appropriate, what is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches? Optimistic approach Conservative approach Minimax approach (d) 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. What option should Amy choose using the expected value approach? (e) Develop a risk profile for the decision selected in part (d). What is the most likely cost? $ What is its probability? If required, round your answer to one decimal place. (f) 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. What decision should Amy make using the expected value approach?

Amy Lloyd is interested in leasing a new Honda 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 Hepburn Honda $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 this 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 costs for the three lease options. For example, she figures that the Hepburn Honda lease will cost her 36($299) + $0.15(36,000 - 36,000) = $10,764 if she drives 12,000 miles per year, 36($299) + $0.15(45,000 - 36,000) = $12,114 if she drives 15,000 miles per year, or 36($299) + $0.15(54,000 - 36,000) = $13,464 if she drives 18,000 miles per year. (a) What is the decision, and what is the chance event? Choose the correct answer below. (i) The decision is to select the number of miles Amy will drive and the chance event is the three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive). (ii) The decision is to select the monthly cost and the chance event is the three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive). (iii) The decision is to select the best lease option from three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive) and the chance event is the number of miles Amy will drive. (iv) The decision is to select the best lease option from three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive) and the chance event is the monthly cost that Amy will incur. (b) Construct a payoff table for Amy's problem. Actual Miles Driven Annually Dealer 12,000 15,000 18,000 Hepburn Honda $ $ $ Midtown Motors $ $ $ Hopkins Automotive $ $ $ (c) If Amy has no idea which of the three mileage assumptions is most appropriate, what is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches? Optimistic approach Conservative approach Minimax approach (d) 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. What option should Amy choose using the expected value approach? (e) Develop a risk profile for the decision selected in part (d). What is the most likely cost? $ What is its probability? If required, round your answer to one decimal place. (f) 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. What decision should Amy make using the expected value approach?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 30P

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Related questions

Question

Dealer	Monthly Cost	Mileage Allowance	Cost per Additional Mile
Hepburn Honda	$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 this 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 costs for the three lease options. For example, she figures that the Hepburn Honda lease will cost her 36($299) + $0.15(36,000 - 36,000) = $10,764 if she drives 12,000 miles per year, 36($299) + $0.15(45,000 - 36,000) = $12,114 if she drives 15,000 miles per year, or 36($299) + $0.15(54,000 - 36,000) = $13,464 if she drives 18,000 miles per year.

(a)

What is the decision, and what is the chance event? Choose the correct answer below.

(i)	The decision is to select the number of miles Amy will drive and the chance event is the three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive).
(ii)	The decision is to select the monthly cost and the chance event is the three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive).
(iii)	The decision is to select the best lease option from three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive) and the chance event is the number of miles Amy will drive.
(iv)	The decision is to select the best lease option from three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive) and the chance event is the monthly cost that Amy will incur.

(b)

Construct a payoff table for Amy's problem.

	Actual Miles Driven Annually
Dealer	12,000	15,000	18,000
Hepburn Honda	$	$	$
Midtown Motors	$	$	$
Hopkins Automotive	$	$	$

(c)

If Amy has no idea which of the three mileage assumptions is most appropriate, what is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches?

Optimistic approach
Conservative approach
Minimax approach

(d)

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. What option should Amy choose using the expected value approach?

(e)

Develop a risk profile for the decision selected in part (d). What is the most likely cost?

What is its probability?

If required, round your answer to one decimal place.

(f)

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. What decision should Amy make using the expected value approach?

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