HMV Limited and a movie studio have decided to sign a revenue-sharing contract for movie DVDs. Each DVD costs the studio $2 to produce. The DVD will be sold to HMV for $3. HMV in turn prices a DVD at $15 and forecasts demand to be normally distributed, with a mean of 8,000 and a standard deviation of 2,800. HMV will share 35% of the revenue with the studio, keeping 65% for itself. There is a single selling period for the DVDs. Any unsold DVDs at the end of the selling period are discounted to $1, and all can be sold at this price. Money made from discounted DVDs is kept by HMV.

(a) How many DVDs should HMV order?

(b) How many DVDs does HMV expect to sell at a discount?

(c) What is the profit that the studio expects to make?

The studio's profit includes the profit obtained from the DVDs that HMV orders from them, plus the income obtained from the revenue that HMV shares with them