A department store is running a promotion one Saturday by giving out coupons for $10 of free merchandise. Based on the data collected in the past, only one-fourth of customers who shop on that Saturday use the coupon but do not purchase any other merchandise. However, one-third of customers purchase $40 in merchandise and then use the coupon. Another one-third of customers use the coupon after ringing up a total of $75 in merchandise. The remainder of customers who come in the store do not take advantage of the promotion at all.
a) Find the expected value of the promotion per customer for the department store.
b) If the store has 720 customers on the promotional Saturday, what is the expected revenue for the day?