2. A publisher sells books to Barnes & Noble (B&N) at $40 each. The marginal production cost for the publisher is $20 per book. B&N prices the book to its customers at $50 and expects demand over the next two months is normally distributed with mean 1000 and standard deviation 500. B&N places a single order with the publisher for delivery at the beginning of the two- month period. Currently, B&N discounts any unsold books at the end of two months down to $10, and any books that did not sell at full price sell at this price. a). How many books should B&N order? b). If the publisher and B&N were vertically integrated, what is the optimal production quantity for the entire system? c). Suppose the publisher and B&N still operate as two separate entities. But now the publisher buys back any unsold books from B&N at a price of $35 per book, and sells them at the discount price of $10. Under this arrangement, how many books will B&N order