The Johnson Manufacturing Company operates six identical machines that are serviced by a single technician when they break down. Breakdowns occur according to the Poisson distribution and average 0.03 breakdowns per machine operating hour. Average repair time for a machine is five hours and follows the exponential distribution.
(a) What percentage of the technician's time is spent repairing machines?
(b) On average, how long is a machine out of service because of a breakdown?
(c) On average, how many machines are out of service?
(d) Johnson wants to investigate the economic feasibility of adding a second technician. Each technician costs the company $18 per hour. Each hour of machine downtime costs $120. Should a second technician be added?