ssignment Amy Loyd is interested in leasing a new Honda and has contacted three
ID: 3197512 • Letter: S
Question
ssignment Amy Loyd 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 Hepburn Honda Midtown Motors Hopkins Automotive Monthly Cost $299 $310 $325 Mileage Allowance 36,000 45,000 54,000 Cost per Additional Mile 0.15 $0.20 $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 kver 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 milles 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). (Hepburn Honda, Midtown Motors, and Hopkins Automotive). Midtown Motors, and Hopkins Automotive) and the chance event is the number of miles Amy (ii) The decision is to select the monthly cost and the chance event is the three alternatives (iii) The decision is to select the best lease option from three alternatives (Hepburn Honda, 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 Option (iil) (b) Construct a payoff table for Amy's problem. Actual Miles Driven AnnuallExplanation / Answer
e) The most likely cost if we choose Midtown Motors is 11160, with probability 0.5+0.4=0.9
f) Now if the probabilities are 0.3 0.4 and 0.3
The expected cost for Hepburn Honda is 0.3(10764)+0.4(12114)+0.3(13464)=12114
The expected cost for Midtown Motors is 0.3(11160)+0.4(11160)+0.3(13050)=11727
The expected cost for Hopkins Automotive is 0.3(11700)+0.4(11700)+0.3(11700)=11700
So she should choose Hopkins Automotive
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