A publisher sells books to Barnes & Noble at $15 each. The unit production cost for the publisher is $3 per book. Barnes & Noble prices the book to its customers at $28 and expects demand over the next two months to be normally distributed, with a mean of 15,000 and a standard deviation of 4,000. 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 $4, 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 above?
Use the following information to solve parts c) and d). A plan under discussion is for the publisher to refund Barnes & Noble $6 per book that does not sell during the two-month period. Because Barnes & Noble shares the point-of-sales data with the publisher, the publisher does not require Barnes & Noble to return all unsold books for verification purpose. As before, Barnes & Noble will discount them to $4 and sell any that remain. c) 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 during the two-month period? [Hint: Since Barnes & Noble gets a refund of $6 from the publisher for each unsold book as well as a $4 of clearing each unsold book after the two-month period, Co = c – b - SR. Moreover, SM = 0] d) What is the expected profit for the publisher under the plan and given Barnes & Noble’s actions in part c)?