. A certain shop has three identical machines that are operated continuously except when they are broken down. Because they break down fairly frequently, the top- priority assign- ment for a full-time maintenance person is to repair them whenever needed. The mean failure rate of each machine is 3 (three times per day), and the repair person is able to repair the broken down machines at a rate of 2 per day, on average. (a) Develop the rate diagram for this Markov chain. (b) Write down time-dependent ordinary differential equations for this Markov chain. (c) Construct the steady-state equations. (d) Determine the the steady-state probabilities.