Question 4

The owner of a Chinese restaurant is deciding whether to prepare Small (S), Medium (M) and Large (L) amount of live crabs in the morning of a particular day. S, M, L supplies of live crabs, costing $2,000, $3,800 and $5,500, are enough for serving exactly 15, 30 and 45 customers respectively. From past experience, the probability of having 15, 30 and 45 customers ordering live crabs are 25%, 40%, and 35% respectively. Each live crab served at the restaurant generates a revenue of $300.

If the demand exceeds the supply, the rejection of each customer who ordered a live crab will result in a loss of $50 due to ill will. If the supply exceeds the demand, the leftover live crabs will be trashed at a neglectable cost at the end of the day.

a.) Construct the payoff table for this problem.

b.) Which alternative should be chosen under the maximax criterion?

c.) Which alternative should be chosen under the maximin criterion?

d.) Which alternative should be chosen under the maximum likelihood criterion?

e.) Determine the expected value of perfect information (EVPI)?