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The Jazzfest occurs over 3 evenings of performances every year, Friday, Saturday, and Sunday.
The Jazzfest occurs over 3 evenings of performances every year, Friday, Saturday, and Sunday. The first night features professional dance troupes, while on Saturday and Sunday the performers are more amateurish. This year for the first time, the Festival Director, Bob Smith, has decided to try a risky venture. hewill record the first night's professional performances and produce a DVD overnight to sell to the audiences on Saturday and Sunday. he is not aiming to make a huge profit on this first experiment, but he does not want to throw away money and she will only proceed, if he believes there is a chance to break-even or make a small profit.
Bob has contacted a DVD manufacturer and was quoted the following prices for production costs:
Fixed:
Making a "Master Disk" $4,200.00
Set-up DVD production equipment $2,800.00
Variable unit per DVD produced:
Packaging $1.00
... other manufacturing $3.00
In addition, for each DVD sold, the Festival will have to pay the dance troupes that are recorded on the disk total royalties of $3.00 (per disk sold - not per disk produced). Finally, there will be a one-time cost of $8,000 to the Festival organizers to pay for the initial recording film crews, ads, and vendors to sell the DVDs on Saturday and Sunday. Bob plans to sell each DVD for $14.00. The unsold DVDs have no value and the unsold disks will be destroyed after the Festival is over.
Since the Festival has never marketed DVDs before, it is difficult for Bob to estimate how many disks will be sold. Demand for the DVDs depends mostly on attendance at the Festival - which has varied greatly in the past from 6,000 to 20,000 per festival day - but it also depends on the unknown demand for the DVDs by those who attend. The Director talked to the organizers of other comparable events and came up with the following predictions for sales demand: he estimates that on Saturday there is a 2/3 chance that the demand will be for 1,000 DVDs and a 1/3 chance the demand will be for 3,000. If the Saturday demand is for only 1,000, then the Sunday demand is also likely to be low. In this case, bob estimates that the demand on Sunday would be either 1,000 or 3,000 with probabilities ¾ and ¼ respectively. On the other hand, if the Saturday demand is high (3,000), he estimates the Sunday demand will be either 1,000 or 3,000 with probabilities ¼ and ¾ respectively.
PART 1: Assume that bob must make a one-time decision on Friday night about how many disks to produce to sell on the next two days (Saturday and Sunday). Using the tentative figures supplied above, answer the following questions. remember bob is smart, but does not have your background in decision analysis. (1A) What is the probability the demand for DVDs will be exactly 4,000 over both Saturday and Sunday sales combined? (1B) How many DVDs should the Festival produce after the Friday performance to maximize Expected Monetary Value? (1C) And, what is the EMV of the best production plan (your answer to 1B)?
PART 2: Now assume that bob has more flexibility and can make a decision on Friday about how many disks to produce to sell on Saturday (she must produce a minimum of 1,000 disks, but can produce more on Saturday night to meet demand on Sunday). Then, after bob sees the Saturday sales, he can make a second decision how many disks to produce on Saturday night to sell on Sunday (he can decide to produce anywhere from 0 to 6000 additional disks, in addition to the original Friday night production of 1,000 or more disks). If his goal is to maximize expected profits from the DVD endeavor, what production strategy should he follow: How many disks should he produce on Friday to sell on Saturday? How should he use the sales demand information on Saturday to decide how many disks to produce Saturday night to sell on Sunday? All of the numbers in the original problem statement still apply, and remember that disks unsold at the end of the day on Sunday have no value. (2A) What production plan maximizes bob's expected dollar profits? (2B) What is the expected overall profit from that plan?
