8. Consider a barbershop with two chairs, two barbers, and no room for customers to wait. Say that the state of the system is the number of customers in the shop: 0,1 , or 2 . If there is an empty chair when a customer arrives, he enters the shop and his haircut begins. If both chairs are occupied when he arrives, he does not enter the shop. As soon as a customer's haircut is completed, he instantaneously leaves the shop. The barbers do not assist one another when there is only one customer in the shop. On the average, a customer arrives every ten minutes, and each haircut takes an average of fifteen minutes. a. Set up the transition diagram and steady-state equations. b. Solve the steady-state equations for the distribution of the number of customers in the shop. c. Calculate the expected number of busy barbers. d. Calculate the expected number of customers turned away per hour. e. Notice in part d above that some potential customers are turned away