8. Bob Farrell, owner of Farrell Motors, is trying to decide whether to buy an insurance policy to cover hail damage on his inventory of more than 200 cars and trucks.

Thunderstorms occur frequently, sometimes producing golfball-sized hailstones that can damage automobiles severely. Bob estimates the potential damage from hail in the next year as:

Hail Damage (in $1000s)

0 15 30 45 60 75 90 105

Probability 0.25 0.08 0.10 0.12 0.15 0.12 0.10 0.08

Bob is considering the following three alternatives for dealing with this risk:

Bob can buy an insurance policy for $47,000 that would cover 100% of any losses that occur.

Bob can buy an insurance policy for $25,000 that would cover all losses in excess of $35,000.

Bob can choose to self-insure, in which case he will not have to pay any insurance

premium but will pay for any losses that occur.

a. Construct a payoff matrix for this problem.

b. What decision should be made according to the maximax decision rule?

c. What decision should be made according to the maximin decision rule?

d. What decision should be made according to the minimax regret decision rule?

e. What decision should be made according to the EMV decision rule?

f. What decision should be made according to the EOL decision rule?