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 places 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. What is the corresponding fill rate?
g. How many books does Borders expect to sell at a discount?
h. The marginal production cost for the publisher is $1 per book. How much profit does the publisher make given Borders' actions?