12. Print Shop. A small print shop has 3 machines and 3 repairmen (any repairman can work on any machine, but only one may work on a machine at a time). Data suggests that the amount of time each machine works before needing repairs is exponentially distributed with a mean of 10 hours; the amount of time required for a single repairman to fix one machine is exponentially distributed with a mean of 8 hours. a. Model the above scenario as a CTMCdefine the random variable, the time index, and the state space. b. Explain how this scenario satisfies the requirements of a Markov chain. c. Determine the transition rates and develop both the rate diagram and the infinitesimal generator matrix (Q). d. Calculate the steady-state probabilities. e. If repairmen are paid $100/hr, what is the expected cost paid-out over a 40-hour week?