Problem 5 (10 points) Sherry's 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 $100.00. The publisher sells the book to Sherry at $75.00. Sherry will dispose of all of the unsold copies of the book at 50% off the retail price, at the end of the season. Sherry estimates that demand for this book during the season is normally distributed with mean 1000 and standard deviation 100 . a. How many copies should Sherry order from the publisher to maximize her expected profit? [4 pts] b. The publisher is thinking of offering the following scheme to Sherry. At the end of the season, the publisher will buy back unsold copies at a pre-determined price of $70.00. However, Sherry would have to bear the costs of shipping unsold copies back to the publisher at $5.00 per copy. What is the quantity that Sherry should order, to maximize her expected profits? What is the probability of returning unsold copies to the publisher? [6 pts]