Top Gun Records and several movie studios have decided to sign a revenue-sharing contract for DVDs. Each DVD costs the studio $2 to produce.

The DVD will be sold to Top Gun for $3. Top Gun in turn prices a DVD at $15 and forecasts demand to be normally distributed, with a mean of 5,000 and a standard deviation of 2,000. Any unsold CDs are discounted to $1, and all sell at this price. Top Gun will share 35 percent of the revenue with the studio, keeping 65 percent for itself.

a. How may CDs should Top Gun order?

b. How many CDs should Top Gun expect to sell at a discount?

c. What is the profit that Top Gun expects to make?

d. What is the profit that studio expects to make?