2. (10 pts) Topgun Records and several movie studios have decided to sign a reve
ID: 334965 • Letter: 2
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 to produce. The CD will be sold to Topgun for $1.5. Topgun in turn prices a CD at S12 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 S0.50, and all sell at this price. Topgun will share 45 percent of the revenue with the studio, keeping 55 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?Explanation / Answer
cost of overage (Co) = Cost - Salvage value = 1.5 - 0.5 = 1 (Since CD sold to topgun costs 1.5, and salvage value 0.5)
Cost of underage (Cu) = Selling price- cost = 12 -1.5 = 10.5
Critical ratio of probability of selling highest = Cu/(Cu + Co)
= 10.5/(10.5 + 1.5)
= 10.5/12
= 0.875
now using standard normal distribution table, we find the z-score for probability of 0.875
z = 1.15
a) average demand (M) = 5000
standard deviation of average demand (s) = 2000
order quantity = M + z*s = 5000 + 1.15*2000 = 5000 + 2300 = 7300
order quantity = 7300
b) 87.5% of the order quantity is expected to be at a full price = 87.5%*7300 = 6387.5
Hence expected sales at discount = 7300 - 6387.5 = 912.5
c) Profit = full price sales*10.5 - discount sales*1 (since profit 10.5, and discount causes loss of 1)
= 6387.5*10.5 - 912.5*1
= 67068.75 - 912.5
= 66156.25
d) 45% with revenue sared with studio.
total revenue = full price sales*12 + discoount price sales*0.5
= 6387.5*12 + 912.5*0.5
= 76650 +456.25
= 77106.25
45% of revenue shared with studio = 77106.25*45% = 34697.8125
cost for studio to make 7300 CDs = 1*7300 = 7300
Profit for studio = 34697.8125 - 7300 = 27397.8125
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