Dan’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 produces the book at the cost of $16 per unit and sells it to Dan at $20. The book retails at $28. Dan will dispose of all of the unsold copies of the book at 50% 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 1000 and a standard deviation of 250.

a.     What is the quantity that Dan should order to maximize his expected profit? (part b and c??)

ANS: 1045 copies

underage cost, Cu= 28-20=8

overage cost, Co-20-28/2=6

critical ratio= Cu/(Cu+Co) =8/14 =0.5714

z= 0.18

b.    Imagine the integrated supply chain where the publisher and Dan make decisions as if they are in a single firm. What is the quantity that the integrated firm should order to maximize their expected profit? (20 points)

c. The optimal order quantity in part b can be considered as the first-best solution for the supply chain. However, Dan found the integration with the publisher is not possible due to other financial issues. Alternatively, Dan is thinking of offering the following scheme to the publisher. At the end of the season, the publisher will buy back unsold copies at a pre-determined price of $r. How should Dan set the return price $r so that the optimal order quantity under this scheme is equal to the first-best solution in part b?