Broke & Down has several hundred machines in its large manufacturing facility as it uses the PWP concept (plant-within-a-plant). Ray Pear, Manager of Maintenance and Chief Mechanic for the Broke & Down Machine Shop, says that broken machines arrive at the repair facility according to a Poisson pattern at the average rate of 2 per 8-hour day. Ray likes to remind his boss, Mr. I. M. Broke, that since he is such a master mechanic he is the only person needed to repair the broken machines, and he can repair a machine in just 2 hours on average. Furthermore, the repair time follows an exponential distribution, and Ray repairs the machines in the order in which they break down. Assuming that the machine shop operates 8 hours per day:
(a) if a machine breaks down, what is the probability that Ray can begin work on it immediately?
(b) on average, how long is a broken machine out of service?
(c) on average, how many machines are awaiting repair?
(d) Mr. Churchill Down, co-owner of the machine shop is concerned that too much productive time is being lost due to machine break downs. He agrees that Ray is a super mechanic but also thinks that Ray needs help so the shop would have less downtime waiting for repairs. Churchill knows of Ray's son Desmond, often called Des for short. Des is also a master mechanic and Churchill has been considering hiring Desmond for some time if it is economically feasible. Master mechanics are paid $20 per hour, and the machines produce revenue at $60 per hour