A publisher sells books to Barnes & Noble at $12 each. The marginal production cost for the publisher is $1 per book.

Barnes & Noble prices the book to its customers at $24 and expects demand over the next two months to be normally distributed, with a mean of 20,000 and a standard deviation of 5,000. Barnes & Noble places a single order with the publisher for delivery at the beginning of the two-month period.

Currently, Barnes & Noble discounts any unsold books at the end of two months down to $3, and any books that did not sell at full price sell at this price.

a. How many books should Barnes & Noble order? What is its expected profit? How many books does it expect to sell at a discount?

b. What is the profit that the publisher makes given Barnes

& Noble’s actions?

c. A plan under discussion is for the publisher to refund Barnes & Noble $5 per book that does not sell during the two-month period. As before, Barnes & Noble will discount them to $3 and sell any that remain. Under this plan, how many books will Barnes & Noble order? What is the expected profit for Barnes & Noble? How many books are expected to be unsold? What is the expected profit for the publisher? What should the publisher do?