Paul, the administrator at Mercy Hospital emergency room faces the problem of providing treatment for patients who arrive at different rates during the day. There are 4 doctors available to treat patients when needed. If not needed, they can be assigned other responsibilities or else rescheduled to work at other hours. It is important to provide quick and responsive treatment, and Stephen feels that, on the average, patients should not have to sit in the waiting area for more than 30 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 pattern for a typical day is as follows: Time Arrival Rate 9 A.M. 3 P.M. 9 patients/hour , 3 P.M. 8 P.M. 6 patients/hour, 8 P.M. midnight 14 patients/hour

Arrivals follow a Poisson distribution, and treatment times, 12 minutes on the average, follow the negative exponential pattern.

a. How many doctors should be on duty during the 9 AM to 3 PM to maintain the level of patient care expected?

b. How many doctors should be on duty during the 3 PM to 8 PM to maintain the level of patient care expected?