Problem 1: Consider that a new novel will begin to sell at a local bookstore next month. The bookstore must decide how many copies of the book to order and stock before demand realization and cannot re-order again. The book will be sold a specified period (two months for example), after which all copies will be sold to a paper-recycling company as scrap. The novel will be sold to customers for $20 per copy. The publisher charges the bookstore a wholesale price of $10 per copy. For each copy ordered by the bookstore, the publisher incurs raw-material costs of $3. The demand D for the novel during the sales season is a normal random variable, where D~N(1500,300). Unsold books are sold to a recycling company for $1 each. a) What is the bookstore's optimal order quantity? b) Given any order Q > 0, what are the expected profits for the bookstore, publisher, and the entire supply chain? c) What is the expected profit of the entire supply chain under the optimal order quantity of the bookstore? d) What is the order quantity that maximizes the expected profit for the entire supply chain? What is the expected profit for the entire supply chain under this optimal order quantity? e) Suppose that the publisher offers the bookstore a buyback contract with a buyback price $6. What value of the wholesale price w will coordinate the supply chain? What is the fraction of profit allocated to the bookstore? f) What value of the buyback price b gives the bookstore all the profit? What value of b gives the publisher all the profit? g) Suppose that the publisher offers the bookstore a revenue sharing contract in which the bookstore keeps 60% of the revenue and gives 40% to the publisher. What value of the wholesale price w will coordinate the supply chain? What is fraction of supply chain profit allocated to the bookstore? h) Let f denote the fraction of revenue shared by the bookstore. What value off gives the bookstore all the profit? What value of f gives the publisher all the profit? Problem 1: Consider that a new novel will begin to sell at a local bookstore next month. The bookstore must decide how many copies of the book to order and stock before demand realization and cannot re-order again. The book will be sold a specified period (two months for example), after which all copies will be sold to a paper-recycling company as scrap. The novel will be sold to customers for $20 per copy. The publisher charges the bookstore a wholesale price of $10 per copy. For each copy ordered by the bookstore, the publisher incurs raw-material costs of $3. The demand D for the novel during the sales season is a normal random variable, where D~N(1500,300). Unsold books are sold to a recycling company for $1 each. a) What is the bookstore's optimal order quantity? b) Given any order Q > 0, what are the expected profits for the bookstore, publisher, and the entire supply chain? c) What is the expected profit of the entire supply chain under the optimal order quantity of the bookstore? d) What is the order quantity that maximizes the expected profit for the entire supply chain? What is the expected profit for the entire supply chain under this optimal order quantity? e) Suppose that the publisher offers the bookstore a buyback contract with a buyback price $6. What value of the wholesale price w will coordinate the supply chain? What is the fraction of profit allocated to the bookstore? f) What value of the buyback price b gives the bookstore all the profit? What value of b gives the publisher all the profit? g) Suppose that the publisher offers the bookstore a revenue sharing contract in which the bookstore keeps 60% of the revenue and gives 40% to the publisher. What value of the wholesale price w will coordinate the supply chain? What is fraction of supply chain profit allocated to the bookstore? h) Let f denote the fraction of revenue shared by the bookstore. What value off gives the bookstore all the profit? What value of f gives the publisher all the profit