Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvania. He must decide on

how many copies to order of a new book, Power and Self-Destruction, and expose on a famous politician's

lurid affairs. Interest in the book will be intense at first and then fizzle quickly away as attention turns to

other celebrities. The book's retail price is $20 and the wholesale prices 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 mean 200 and standard deviation 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? (Hint: use the Normal tables to calculate

the probability that demand is greater than 400 units. You first need to convert 400 to a z value: z = (400 -

200)/80 = 2.50.

b. Dan considers a book a "dog" if it sells less than 50 percent of his mean forecast. What is the probability

that this expose is a "dog"?

d. What order quantity maximizes Dan's expected profit?

e. Dan prides himself on good customer service. In fact, his motto is "Mc Clure's got what you want to

read." How many books should Dan order if he wants to achieve a 95 percent in-stock probability?

Hint: F(Q) = Prob(Demand <= Q) = 0.95

You have the probability, find "z" (don't forget to use the "round-up rule." Choose the "z" which gives the

higher order quantity) and convert to Q: Q = + z

f. If Dan orders the quantity chosen in part e to achieve a 95 percent in-stock probability, then what is the

probability that he will be out of stock?

Hint: 1 - F(Q) = Prob(Demand > Q)