The administrator at the City Hospital’s emergency room faces a problem of providing treatment ...

        The administrator at the City Hospital’s emergency room faces a   problem of providing treatment for patients that arrive at different rates   during the day. There are four doctors available to treat patients when   needed. If not needed, they can be assigned to other responsibilities (for   example, lab tests, reports, x-ray diagnoses, etc.) or else rescheduled to   work at other hours.   It is   important to provide quick and responsive treatment, and the administrator   feels that, on the average, patients should not have to sit in the waiting   area for more than five 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:   Time                          Arrival Rate     9 a.m. – 3   p.m.               6   patients/hour    3 p.m. – 8   p.m.           4 patients/hour    8 p.m. –   Midnight           12 patients/hour    __________________________________________    These   arrivals follow a Poisson distribution, and treatment times, 12 minutes on   the average, follow the exponential pattern.   How many   doctors should be on duty during each period in order to maintain the level   of patient care expected