A publisher sells books to Borders at $12 each. Borders prices the book to its customers at $24 and expects demand over the next two months to be normally distributed, with a mean of 20,000 and a standard deviation of 5,000. Borders place a single order with the publisher for delivery at the beginning of the two-month period. Currently, Borders discounts any unsold books at the end of two months down to $3, and any books that did not sell at full price sell at this price.

a. Borders will consider this book to be a bestseller if it sells 25,000 copies. What is the probability that it is a bestseller?

b. Borders will consider this book to be a flop if it sells less than 50% of the mean forecast. What is the probability that it is a flop?

c. What is the probability that the book will sell within 20% of its mean forecast?

d. What order quantity maximizes Borders’ expected profit?

e. How much is this expected profit?

f. How many books does Borders expect to sell at a discount?

g. The marginal production cost for the publisher is $1 per book. How much profit does the publisher make given Borders’ actions?