Please answer (b) step-by-step so I can understand it. Thanks!

Question 1. (Book Store) 80 points Dan's Independent Book Store is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season. The book retails at $28, and the publisher's production cost is $15 per book. At the end of the season, Dan can dispose of all of the unsold copies of the book at 50% off the retail price, whereas the publisher can dispose of all of the unsold copies at $10 each. Dan estimates that demand for this book during the season is Normal with a mean of 1000 and a standard deviation of 250. The publisher has offered the following two schemes to Dan. () The publisher sells the book to Dan at $19. At the end of the season, they will buy back unsold copies at a pre-determined price of $16. However, Dan would have to bear the costs of shipping unsold copies back to the publisher at $1 per copy. The publisher sells the book to Dan at $22. At the end of the season, they will not buy back the unsold copies. b. What is the quantity that Dan should order under each scheme, to maximize his expected profits