One mechanic services 5 drilling machines for a steel plate manufacturer. Machines break down on an average of once every 6 working days, and breakdowns tend to follow a Poisson distribution. The mechanic can handle an average of one repair job per day. Repairs follow an exponential distribution.

a) On the average, how many machines are waiting for service?

b) On the average, how many drills are in running order?

c) How much would waiting time be reduced if a second mechanic were hired? P ...D.20 Richard Insinga, the administrator at an Onienta Hospital emergency room, faces the problem of providing treatment for patients who arrive at different rates during the day. There are four doctors available to treat patients when needed. If not needed, they can be assigned other responsibilities (such as doing lab tests, reports, X-ray diagnoses) or else rescheduled to work at other hours. It is important to provide quick and responsive treatment, and Richard feels that, on the average, patients should not have to sit in the waiting area for more than 5 minutes before being seen by a doctor. Patients are treated on a first-come, first-served basis and see the first available doctor after waiting in the queue. The arrival pat- tern for a typical day is as follows:Arrivals follow a Poisson distribution, and treatment times, 12 minutes on the average, follow the exponential pattern.

a) How many doctors should be on duty during each period to maintain the level of patient care expected?

b) What condition would exist if only one doctor were on duty between 9 A.M. and 3 P.M. P ...