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  3. 1. suppose that new york fire department receives

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

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Advance Math

1. Suppose that New York fire department receives an average of12 requests for fire engines each hour, and that these requestsoccur according to a Poisson process. Each request causes a fireengine to be unavailable for an average of 12 minutes. To have atleast a 90% chance of being able to respond to a request, how manyfire engines should the fire department have?

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

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