A single repairman looks after both machines 1 and 2. Each time it is repaired, machine i stays up for an exponential time with rate λi , i = 1, 2. when machine i fails, it requires an exponentially distributed amount of time to work with rate µi to complete its repair. The repairman will always service machine 1 when it is down. For instance if machine 1 fails while machine 2 is being repaired, then the repairman will immediately stop work on machine 2 and start on 1. (i) Set up the balance equations for this problem. [9] (ii) Find the proportion of time machine 2 is down