Dazzle Productions is about to launch the latest tour of one of the hottest musical acts of the decade. The concert is to play at huge arenas. Lighting, staging and production affects are the best available, yet very costly. Each time a show is cancelled, Dazzle Productions must absorb an average rescheduling cost of $325,000. This cost includes transportation, lodging, setup and teardown, publicity, and administrative costs.

In order to minimize the necessity to reschedule concert dates, Dazzle productions has asked you to study the benefit of leasing backup sound boards for the tour. The sound board used for this tour costs an average of $5,000 per show to lease and transport. The soundboard has a failure rate of 20%.

If Dazzle Productions wants to minimize the expected cost of rescheduling a show, how many spare sound boards should the tour carry?

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We need to find out how many spare soundboards to bring along.

Let n be the number of spare soundboards we bring along. This will cost us $5 n (in thousands of dollars) to lease and transport. If the one we are using for the show and all of the spares fail we occur an extra cost of the cancelled show of $325. The probability that this happens is equal to .2n+1

Therefore our expected expense per show is equal to: 5n + 325*.2n+1
What we should do is: find the value for n which makes the expected expense as small as possible. This will be the basis for my recommendation of how many spares to bring along....

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