18 Sal’s International Barbershop is a popular haircutting and styling salon near the campus of the University of New Orleans. Four barbers work full time and spend an average of 15 minutes on each customer. Customers arrive all day long, at an average rate of 12 per hour. When they enter, they take a number to wait for the first available barber.

Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed.

(a) What is the probability that the shop is empty?

(b) What is the average number of customers in the barbershop?

(c) What is the average time spent in the shop?

(d) What is the average time that a customer spends waiting to be called to a chair?

(e) What is the average number of customers waiting to be served?

(f) What is the shop’s utilization factor?

(g) Sal’s is thinking of adding a fifth barber. How will this affect the utilization rate?