Dan is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season for his bookstore. The book retails at $28. The publisher sells the book to Dan for $20. The publisher's variable cost per book is $7.5. Dan will dispose of all of the unsold copies of the book at $7 at the end of season. Dan estimates that demand is normal with a mean of 100 and a standard deviation of 42.
The publisher is thinking of offering the following deal to Dan. At the end of the season, the publisher will buy back unsold copies at a pre-determined price of $15. However, Dan would have to bear the costs of shipping unsold copies back to the publisher at $1 per copy.
If Dan orders 108 books to maximize his profit, given the buyback offer, what is Dan's expected profit given the the order quantity of 108?