Dan McClure is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season for his bookstore. The book retails at $28.00. The publisher sells the book to Dan for $20.00. Dan will dispose of all of the unsold copies of the book at 75 percent off the retail price, at the end of the season. Dan estimates that demand for this book during the season is normal with a mean of 100 and a standard deviation of 42.
a. How many books should Dan order to maximize his expected profit?
b. Given the order quantity in part a what is Dan's expected profit?
c. The publisher's variable cost per book is $7.50. Given the order quantity in part a, what is the publisher's expected profit? The publisher is thinking of offering the following deal to Dan. At the end of the season, the publisher will buy back unsold copies at a predetermined price of $15.00. However, Dan would have to bear the costs of shipping unsold copies back to the publisher at $1.00 per copy.
d. How many books should Dan order to maximize his expected profits given the buy- back offer?
e. Given the order quantity in part d, what is Dan's expected profit?
f. Assume the publisher is able on average to earn $6 on each returned book net the publisher's handling costs (some books are destroyed while others are sold at a discount and others are sold at full price). Given the order quantity in part d what is the publisher's expected profit?
g. Suppose the publisher continues to charge $20 per book and Dan still incurs a $1 cost to ship each book back to the publisher. What price should the publisher pay Dan for returned books to maximize the supply chain's profit (the sum of the publisher's profit and Dan's profit)?