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Problem 6: DVD retailer A DVD retailer must place a single advance order for a specific movie with a short store life- cycle of only 1 month. The total consumer demand over this 1 month is estimated to be normally distributed with a mean of 1500 copies and a standard deviation of 400. Each copy costs the retailer 5 and can be sold for 15 to consumers. The retailer has negotiated a buy- back agreement: any unsold copies at the end of the month will be returned to the manufacturer who will then refund the retailer 2 per copy. Q 6.1 - What are the under-and over-stocking costs of a copy of the movie? Q6.2 - How many copies of the movie should the retailer order to maximize its expected profit? Q 6.3 - Suppose that the buy-back contract between the retailer and its supplier is up for renegotiation. What would the per-copy value of the buy-back that would result in 10% increase in the optimal order quantity