What order quantity maximizes dan expected profit

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Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvania. He must decide how many copies to order of a new book, Power and Self-Destruction, an exposé on a famous politician’s lurid affairs. Interest in the book will be intense at first and then fizzle quickly as attention turns to other celebrities. The book’s retail price is $20, and the wholesale price is $12. The publisher will buy back the retailer’s leftover copies at a full refund, but McClure Books incurs $4 in shipping and handling costs for each book returned to the publisher. Dan believes his demand forecast can be represented by a normal distribution with a mean of 200 and a standard deviation of 80.

a) Dan will consider this book to be a blockbuster for him if it sells more than 400 units. What is the probability that Power and Self-Destruction will be a blockbuster?

b) Dan considers a book a “dog” if it sells less than 50 percent of his mean forecast. What is the probability this exposé is a “dog”?

c) What is the probability that demand for this book will be within 20 percent of the mean forecast?

d) What order quantity maximizes Dan’s expected profit?

e) If Dan orders the quantity needed to achieve a 95 percent in-stock probability, what is the probability that some customer won’t be able to purchase a copy of the book?

Reference no: EM132258753

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