A  movie studio sells  the latest movie on DVD to Blockbuster at $10 per DVD.  The marginal production cost for the movie studio is $1 per DVD.  Blockbuster prices each DVD at $20 to its customers.  DVD s are kept on the regular rack for a one-month period, after which they are discounted down to $5, Blockbuster places a one order for DVDs.  Their 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 Blockbuster order?

b.    What is its expected profit?

c.    How many DVDs does it expect to sell at a discount?

d.    What is the profit that the studio makes given Blockbuster's actions?

A plan under discussion is for the studio to refund Blockbuster $4 per DVD that does not sell during the one-month period.  As before, Blockbuster will discount them to $5 and sell any that remain.  

e.    Under this plan, how many DVDs should Blockbuster order?  

f.    What is the expected profit for Blockbuster?  

g.    How many DVDs are expected to be unsold at the end of the month?

h.    What is the expected profit for the studio?  

i.    What should the studio do?