Dans Bookstore and a publisher have decided to sign a revenue-sharing contract for a new book. Each book costs the publisher $5 to print. The book will be sold to Dans Bookstore for $8 per unit. Dans Bookstore in turn prices the book at $20 and forecasts demand to be normally distributed, with a mean of 10,000 and a standard deviation of 4,000. Dans Bookstore will share 30% of the revenue with the publisher, keeping 70% for itself. There is a single selling period for the book, and the bookstore only places one order at the beginning of selling period. Any unsold books at the end of the selling period are discounted to $4, and all can be sold at this price. Money made from discounted books is kept by the bookstore. (a) How many books should the bookstore order? (b) At the optimal order quantity, how many books does the bookstore expect to sell at a discount? (c) What is the profit that the publisher expects to make? (Note that the publishers profit includes the profit obtained from the books that the bookstore orders from them, plus the income obtained from the revenue that the bookstore shares with them.)