Lester Books Inc. is a book retailer that sells NY Times Bestsellers for four weeks and constantly moves on to new books - so, they typically place only one order of a new book. They are deciding how much to order of a new nonfiction book "AI for Business". The publisher will sell it to them at a cost of $20 and they will retail it at a price of $60. They expect that demand for the item is normally distributed with a mean of 500 and standard deviation of 200. Any item left over at the end of the four-week period is sold at a deep discount price that is only 20% of the regular retail price.

a. What is the understocking cost per unit? What is the overstocking cost per unit? How many units of the book should Lester Books order so as to maximize expected profits?

If they order the quantity you estimated in part (a), what is the expected revenue from items sold at the deep discount price?

If they order the quantity you estimated in part (a), what is the expected revenue forgone because they had stockouts?