Question

2. (10 pts) Topgun Records and several movie studios have decided to sign a revenue-sharing contract for CDs. Each CD costs the studio $1.5 to produce. The CD will be sold to Topgun for $2. Topgun in turn prices a CD at $14 and forecasts demand to be normally distributed, with a mean of 6,000 and a standard deviation of 2,000. Any unsold CDs are discounted to $1, and all sell at this price. Topgun will share 40 percent of the revenue with the studio, keeping 60 percent for itself.

a) How many CDs should Topgun order?

b) How many CDs does Topgun expect to sell at a discount?

c) What is the profit that Topgun expects to make?

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

Answer 1

Mean Demand, u = 6000

Standard deviation, s = 2000

Topgun Selling price, p = $14 , Revenue share of ps = 60% * 14 = $8.4

Topgun Cost price, c = $2

Discount value, d = $1

Cost of overordering, Co = c - p = $1

Cost of underordering, Cu = ps - c = $6.4 ( 8.4 is our share -cost)

Critical factor ratio ,= Cu / (Co + Cu) = 6.4 / 7.4 = 0.865

Z-score = 1.102 for Probability = 0.865 (From standard normal distribution table)

a) Hence, CD's to be ordered = 6000 + 2000 * 1.1025 = 8204.88 or 8205 CDs

Rest of the problems are solved in excel with formulas

Expected overstock = Expected to sell at discount

Expected sales = Order - Expected to sell at discount

Formulas