You are planning to rent a car for a one-week vacation. You have the option of buying an insurance that costs $80 dollars for a week. If you do not purchase insurance, you would be personally liable for any damages. You anticipate that a minor collision will cost $2,000, whereas a major accident might cost $16,000 in repairs.Develop a payoff table for this situation. What decision should you make using each strategy?Aggressive (Optimistic)Conservative (Pessimistic)Opportunity Loss You have recently read in a magazine that that the probability of a major accident is 0.05% and that the probability of a minor collision is 0.18%. Construct a decision tree and identify the best expected value decision.

Payoff Table Alternative State of Nature Minor Accident/Collision (Cost) Major Accident/Collision (Cost) Buy Insurance $80 $80 Do not buy insurance $2000 $160001. Aggressive (Optimistic) Alternative State of Nature Minor Accident/Collision (Cost) Major Accident/Collision (Cost) Maximum Buy Insurance $80 $80 80 Do not buy insurance $2000 $16000 2000 In the case of optimistic decision-making, the decision will be to buy insurance as the maximum payoff is 80 (as this is the cost). 2. Conservative (Pessimistic) Alternative State of Nature Minor Accident/Collision (Cost) Major Accident/Collision (Cost) Minimum Buy Insurance $80 $80 80 Do not buy insurance $2000 $16000 16000 The conservative person will also buy the insurance as the best payoff from the all worst payoffs is for buying insurance (as this is the cost) 3. Opportunity Loss In this case, first, we will make a regret-table, in which, for each state of nature, we will find the maximum amount and subtract the payoff from each payoff Regret table: Alternative State of Nature Minor Accident/Collision (Cost) Major Accident/Collision (Cost) Maximum Buy Insurance 0 0 0 Do not buy insurance 2000-80=1920 16000-80=15920 15920 As in this case, the payoff is the cost, we will go for the buying insurance as it has the lowest opportunity cost.Payoff calculation: Buy insurance = (0.0018*80)+(0.0005*80)+(0.9977*80)=$80 Do not buy insurance = (0.0018*2000)+(0.0005*16000)+(0.9977*0)=$11.6 Hence, the person should not buy insurance Please note that the probability is (Percentage/100). So it is taken as 0.0018(0.18/100). Probability of no accident = 1 - 0.0018-0.0005 = 0.9977 As this is a cost problem, we need to select the least cost payoff. Hence, do not buy insurance is the correct answer.

Answered: You are planning to rent a car for a…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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You are planning to rent a car for a one-week vacation. You have the option of buying an insurance that costs $80 dollars for a week. If you do not purchase insurance, you would be personally liable for any damages. You anticipate that a minor collision will cost $2,000, whereas a major accident might cost $16,000 in repairs.

Develop a payoff table for this situation. What decision should you make using each strategy?

Aggressive (Optimistic)
Conservative (Pessimistic)
Opportunity Loss

You have recently read in a magazine that that the probability of a major accident is 0.05% and that the probability of a minor collision is 0.18%. Construct a decision tree and identify the best expected value decision.

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