A publisher sells books to Borders at $10 each. Borders prices the book to its customers at $17 and expects demand over the next two months to be normally distributed, with a mean of 50,000 and a standard deviation of 30,000. 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 $5, 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 100,000 copies. What is the probability that it is a bestseller?
b. What order quantity maximizes Borders' expected profit?
c. How much is this expected profit?
d. What is the corresponding fill rate?
e. The marginal production cost for the publisher is $3 per book. How much profit does the publisher make given Borders' actions?