3. m automatic machines are serviced by a singale repairperson. If at time t, a chine is working, the probability that it will break down in (t, t + 6) is Ad to A machine which breaks down is serviced immediately unless the repairperson servicing another machine in which case the break down machines form a wait line for service. The time it takes a repairperson to repair a machine is exponenti distributed with mean 1/p. Let X, be the number of machines NOT working time t. (a) Show that {Xtheso is a continuous homogenerous MC satisfying the Basic sumption and find the Q-matrix. (b) Find the stationary dist of Xt. (c) When m = 2, find the maximum ratio of A/p so that the proportion that marchines work at time t is less 0.05 in the long run