A movie studio sells the lates

A movie studio sells the latest movie on DVD to Videos RUs
at $10 per DVD. The marginal production cost for the movie studio is $1 per
DVD. Videos RUs 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. Videos RUs 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 Videos RUs 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 Videos
RUs’ actions?

c. A plan under discussion is for the studio to refund
Videos RUs $4 per DVD that does not sell during the one-month period. As
before, Videos RUs will discount them to $4.99 and sell any that remain. Under
this plan, how many DVDs should Videos RUs order? What is the expected profit
for Videos RUs? 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?

 
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