Question: A soap producer has two types of customer, A and B. Each will buy at most 1 pound per week. Type A customers will pay at most $6 for it, and Type B will pay at most $4. Production cost is $2 per pound. Using a discount coupon costs a Type A customer $1.50 to keep track of the coupon, and a Type B customer nothing.
a. What price should the producer charge the Type As?
b. At this price, how large must a coupon discount be before Type Bs choose to use them?
c. What is the maximum discount a coupon can offer before Type As begin using them?