Alice’s Independent Book Store is trying to decide on how many copies of a book to purchase at the start of the upcoming

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Alice’s Independent Book Store is trying to decide on how many copies of a book to purchase at the start
of the upcoming selling season. The publisher incurs a production cost of $20 for every copy of the book.
The book sells at retail price $100. Any unsold copies at the end of the season have zero salvage value. It
is estimated that demand for this book during the season is normally distributed with mean 1000 and
standard deviation 100.
a. Suppose the publisher offers a wholesale price contract with the wholesale price $40. What is the
book store’s optimal order quantity?
b. The publisher is considering a revenue-sharing contract. For each copy sold to the end customer, thepublisher can get $50 from the bookstore. How much should the supplier charge the retailer for thewholesale price so that the total supply chain’s expected profit can be maximized?
b. The publisher is considering a revenue-sharing contract. For each copy sold to the end customer, the
publisher can get $50 from the bookstore. How much should the supplier charge the retailer for the
wholesale price so that the total supply chain’s expected profit can be maximized?
c. Instead of the revenue-sharing contract in part (b), the publisher is now considering a returnspolicy. Now the publisher sells the book to Alice at the wholesale price $50. At the end of theseason, the publisher will buy back unsold copies at a pre-determined refund of $r. However, Alicewould have to bear the costs of shipping unsold copies back to the publisher at $4 per copy. What isthe value of r under which the retailer’s optimal order quantity also maximizes the total supplychain’s expected profit?
c. Instead of the revenue-sharing contract in part (b), the publisher is now considering a returns
policy. Now the publisher sells the book to Alice at the wholesale price $50. At the end of the
season, the publisher will buy back unsold copies at a pre-determined refund of $r. However, Alice
would have to bear the costs of shipping unsold copies back to the publisher at $4 per copy. What is
the value of r under which the retailer’s optimal order quantity also maximizes the total supply
chain’s expected profit?
d. Suppose the publisher and bookstore use the optimal revenue sharing contract proposed inquestion(b). What is the expected profit for the bookstore and the publisher?
d. Suppose the publisher and bookstore use the optimal revenue sharing contract proposed in
question(b). What is the expected profit for the bookstore and the publisher?