PLEASE SHOW STEP BY STEP

14. (12 points) You must show your detailed work to get credit in this question. You can submit your numerical work either via Excel Model or typed-form showing the step-by step analysis. Dan McClure 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 $120. The publisher sells the book to Dan for $60. Dan will dispose of all of the unsold copies of the book at 80% off the retail price, at the end of the season. Dan estimates that demand for this book during the season is Normal with a mean of 100 and a standard deviation of 30. The publisher offers the following deal to Dan. At the end of the season, the publisher will buy back unsold copies at a pre-determined price of $40. However, Dan would have to bear the costs of shipping unsold copies back to the publisher at $4 per copy. a. How many books should Dan order to maximize his expected profits given the buyback offer? b. Given the order quantity in part a, what is Dan's expected profit