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In: Advanced Math

1. Suppose that New York fire department receives an average of 12 requests for fire engines...

1. Suppose that New York fire department receives an average of 12 requests for fire engines each hour, and that these requests occur according to a Poisson process. Each request causes a fire engine to be unavailable for an average of 12 minutes. To have at least a 90% chance of being able to respond to a request, how many fire engines should the fire department have?

2. Two one-barber shop sit side by side in New York. Each shop can hold a maximum of 5 people, and any potential customer who finds a shop full will not wait for a haircut. Barber 1 charges $18 per haircut and takes an average of 20 minutes to complete a haircut. Barber 2 charges $13 per haircut and takes 15 minutes to complete a haircut. On average 12 potential customers arrive per hour at each barber shop. Of course, a potential customer become an actual customer only if he or she finds that the shop is not full. Assuming that inter-arrival times and haircut times are exponential, which barber will earn more money?

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Expert Solution

Colby Messinger answered 1 year ago
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