HW-19

Problem 1

(Calculate to 6 decimal places)

Two one-barber shops sit side by side in Memorial Union. 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 20minutes to complete a haircut. Barber 2 charges $13 per haircut and takes 15 minutes to complete a haircut. On average, 12potential customers arrive per hour at each barbershop. Of course, a potential customer becomes an actual customer only if they find that the shop is not full. Assuming that inter-arrival times and haircut times are exponential, how much is barber twos hourly income?

(a) Barber 1:

(b) Barber 2:

Problem 2

(Calculate to 4 decimal places)

Suppose that the Grand Forks 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 12minutes.

(a) If the Grand Forks fire department has one fire engine, what is the probability that the request will not be fulfilled? (3 points)

(b) If the Grand Forks fire department has three fire engines, what is the probability that the request will not be fulfilled?

(c) To have at least an 80% chance of responding to a request, how many fire engines should the fire department have?