Redfilm records and a movie studio have decided to sign a revenue sharing contra

Question

Redfilm records and a movie studio have decided to sign a revenue sharing contract for CDs. Each CD costs the studio $3 to produce. The CD will be sold to Redfilm for $4. Redfilm in turn prices a CD at $ 15 and forecasts demand to be normally distributed, with a mean of 4,000 and a standard deviation of 1,000. Redfilm will share 30% of the revenue with the studio, keeping 70% for itself. Any unsold CDs are disconnected to $1.0, and all sell at this price.

1-How many CDs should Redfilm order?

2-How many CD~s dose Redfilm expect to sell at a discount?

3-What is the profit that Redfilm except to make?

4-If Redfilm also needs to share the revenue from the discounted sale with the studio, how many CDs should Redfilm order?

Explanation / Answer

Profit of sold CD=15-4=$11

Loss on unsold CD=4-1=$3

Assuming Red film forecast the demand with 95% confidence

For 95% confidence z=1.64 standard deviation

Thus Expected demand=Mean-1.64*standard deviation=4000-1.64*1000=2360

Redfilm should order 2360 CD with 95% confidence to sell

There is 5% probability that CD will not be sold (As confidence level is 95%)

Thus the number of CD redfilm expect to sell at discount=5%*2360=118

Expected Profit =0.7*2360*11*0.95+2360*(-3)*0.05=$16909.4

If redfilm expect to share the discounted sale with studio then

Expected Profit =0.7*(2360*11*0.95+2360*(-3)*0.05)=$ 17015.6

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