In the carwash center, a maximum of 4 cars are accepted due to the capacity of the facility. There are two workers as Worker X-Worker Y, where Worker X is more experienced one. That is, if X and Y are both available (not busy), the next car-driver will choose Worker X with probability 0.80. If all workers are busy, then they share the same queue (i.e., if there is a car waiting in line, it has no choice, it is served by the first available worker). An average of 2 cars arrive per hour and arrival process follows a Poisson Distribution. Where worker X washes a car in 24 minutes, Worker Y washes in 30 minutes on average and both times are exponentially distributed. a) Define the Markov Chain and write down the state space. b) Draw the transition diagram with the transition rates. c) Compute the steady state probabilities. d) Compute the proportion of time Worker Y is busy. e) What is the average number of cars waiting for the wash? f) On the average, how many cars will be washed per hour?