A factory has three machines and two parallel identical repairmen. The failure time of each machine, independently of the other, is exponentially distributed. The time for a repairman to repair a machine is exponentially distributed. We model this problem with a Continuous Time Markov Chain with states representing the number of nonworking machines (having failure) and solve the limiting probabilities for (π0, π1, π2, π3) as (0.180, 0.404, 0.303, 0.113) respectively.

a) What is the expected number of busy repairmen in the factory?
b) What is the expected number of working machines in the factory?