A movie studio sells the latest movie on DVD to VideosRUs at $10 per DVD. The marginal production cost for the movie studio is $1 per DVD. VideosRUs prices each DVD at $19.99 to its customers. DVDs are kept on the regular rack for a one-month period, after which they are discounted down to $4.99 (a price at which they sell out). VideosRUs places a single order for DVDs. Its current forecast is that sales will be normally distributed, with a mean of 10,000 and a standard deviation of 5,000.

a. How many DVDs should VideosRUs order? What is its expected profit? How many DVDs does it expect to sell at a discount?
b. What is the profit that the studio makes given VideosRUs’ actions?
c. A plan under discussion is for the studio to refund VideosRUs $4 per DVD that does not sell during the one-month period. As before, VideosRUs will discount them to $4.99 and sell any that remain. Under this plan, how many DVDs should VideosRUs order? What is the expected profit for VideosRUs? How many DVDs are expected to be unsold at the end of the month? What is the expected profit for the studio? What should the studio do?