Dan McClure’s Bookstore

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Dan McClure’s Bookstore is trying to decide how many copies of a book to purchase. The publisher charges $20 for the book, which will retail for $28. Unsold copies can be sold after the selling season at 75% off of the retail price. Demand for the book is estimated to be normally distributed with a mean of 100 and a standard deviation of 42.

Using a standard Newsvendor model, Dan finds the expected profit maximizing order quantity is 88, and his expected profit is $456.12. Further, given that the publisher’s cost per book is $7.50, and Dan’s order quantity of 88, the publisher’s profit is $1100.

The publisher is thinking of offering McClure the following deal: At the end of the season the publisher will buy back unsold copies at a set price of $15 per book. McClure would, however, have to bear the cost of shipping unsold copies of $1.00 per book.

a) Now how many books should McClure order?

b) Given the order quantity in part a), now what is Dan’s expected profit?

c) Suppose the publisher is able to salvage $6.00 per returned book net of all handling costs. What is the publisher’s expected profit? (This is just revenue minus cost for the initial sale to Dan, plus revenue minus cost (which will be negative) for the buybacks.)

d) What price should the publisher offer to pay McClure for returned copies to maximize the supply chain’s total profit?

e) Are Dan and the publisher both better off with this buyback price compared to the $15 buyback price originally offered? Show your calculations.

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