Purdue Book Store is trying to decide on how many copies of a book to purchase from the McGraw Hill publisher at the start of a selling season.  The book retails at $28 per copy at the book store, and costs $15 for the book publisher to produce each copy. Purdue Book Store will dispose of all of the unsold copies of the book at 50% off the retail price at the end of the season. 

It is estimated that demand for this book during the season is Normal with a mean of 1000 and a standard deviation of 250. 

We consider the book publisher ("supplier") and the book store ("retailer") as a simple supply chain.

 

1. First, consider the centralized case where the supplier and retailer belong to the same company. What is the optimal quantity Q that the book store should order from the publisher to maximize the total supply chain's profit? Round upQ to integer if necessary. 
2. Then, consider the decentralized case without any coordination. The publisher sells the book to the book store at $21 per copy. Now, what is the optimal quantity Q that the book store should order from the publisher to maximize his own expected profits? Round up Q to integer if necessary.