1. (20 pts) A publisher sells books to Barnes & Noble at $16 each. The unit cost for the publisher is $3 per book. Barnes& Noble prices the book to its customers at $34 and expects demand over the next two months to be normally distributed, with a mean of 30,000 and a standard deviation of 8,000. 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 $2, 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 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 expect to sell at a discount? A plan under discussion is for the publisher to refund Barnes& Noble S3 per book that does 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 $2 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 S3 from the publisher for each unsold book as well as a $2 of clearing each unsold book after the two-month period, Co c-b-SR. Morcover, SM 0] What is the expected profit for the publisher under the plan and given Barnes& Noble's actions irn part c)