A small barbershop, operated by a single barber, has room for at most two customers. Potential customers arrive at a Poisson rate of three per hour, and the successive service times are independent exponential random variables with mean hour. What is

(a) the average number of customers in the shop?

(b) the proportion of potential customers that enter the shop?

(c) If the barber could work twice as fast, how much more business would he do?