The Grotto makes numerous varieties of cheesecakes everyday. Cheesecakes are cut into 12 slices and sold by the slice, but The Grotto has only tracked demand in terms of whole cheesecakes. The distribution of demand is as follows:
Demand 18 19 20 21 22
Probability 0.10 0.20 0.30 0.30 0.10
A whole cheesecake costs $18 to make and sells for $48. Unsold cakes are destroyed.
a) Grotto must decide whether to make 18, 19, 20, 21 or 22 cakes. They have 5 possible decisions and there are 5 possible demand outcomes. Construct a payoff table that shows the profit for each of the 25 possible decision and demand combinations.
b) How many cakes should they make to maximize the expected profit based on Expected Monetary Value criterion?