George Burdell has started a job at Georgia Tech's bookstore. As part of his responsibilities, he must decide how many copies of the book "The Goal" he should order from the publisher for next semester's MGT 3501 class. The book retails for $28, and the publisher sells the book to George for $20 per copy. At the end of the semester, George can sell any unsold copies for a deeply discounted price of $7 per copy. He currently estimates that the book's demand during the semester follows a normal distribution with a mean of 100 and a standard deviation of 42.

Question 1 (10 points)

How many copies of The Goal should George order to maximize his expected profits? What is his expected profit when he orders this quantity?

Question 2 (5 points)

The publisher's cost to print and ship a copy of The Goal to George is $7.50 per copy. Given your order in Question 1, what is the publisher's expected profit?

Question 3(10 points)

The publisher is considering offering George the following deal. At the end of the semester, the publisher will buy back unsold book copies for a pre-negotiated price of $15.00 each. However, George must bear the shipping cost of unsold books back to the supplier at $1.00 per copy.

Given this buy-back offer, how many copies of The Goal should George order to maximize his expected profits? What is his expected profit in this case?

Question 4 (5 points)

Consider the same set-up of Question 3. Assume that the publisher can earn, on average, $6 per returned book. Given the order quantity in Question 3, what is the publisher's expected profit?

Question 5 (5 points)

Suppose the publisher continues to charge $20 per book, and George still incurs a $1 cost to ship each book back to the publisher. What price should the publisher pay George for returned books to maximize the supply chain's profit (the sum of George's profit and the publisher's profit)?