parts a,b,c and d please

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 24. The publisher sells the book to Dan for 18. The publisher's variable cost per book is 12. Dan will dispose of all unsold copies of the book at 6 at the end of the season. Dan estimates that demand is Normal with a mean of 80 and a standard deviation of 10. a. (10 pts) How many books should Dan order to maximize his expected profit? Given this order quantity, what is Dan's expected profit? What is the expected profit of the publisher? Hint: The following formula can be used to calculate the expected profit of a newsboy: Optimal profit =( retail price purchasing cost) MEAN DEMAND (retail price salvage value) x STANDARD DEVIATION x(z) where is the standard normal density (i.e., (z)=21e2z2 ) and z= NORMSINV(critical fractile). 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. b. (10 pts) How many books should Dan order to maximize his expected profits given the buyback offer? Given this order quantity, what is Dan's expected profit? How does it compare to his profit in part a? c. (10 pts) Assume that the publisher can earn 6 on each returned book. What price should the publisher pay Dan for returned books (instead of 15 ) to maximize the supply chain's profit? d. (5 pts) What are the profits for Dan, the publisher, and the supply chain in part c? Who is better off compared to part a