The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a random variable having the probability distribution (x) = 1/6 for x = 0, 1, 2, 3, 4, and 5. He also knows that there is a profit of $1.00 for each cake that he sells and a loss (due to spoilage) of $0.40 for each cake that he does not sell. Assuming that each cake can be sold only on the day it is made, find the baker's expected profit for a day on which he bakes

(a) one of the cakes;

(b) two of the cakes;

(c) three of the cakes;

(d) four of the cakes;

(e) five of the cakes.

How many should he bake in order to maximize his expected profit?