Heavenly Mercy Hospital wants to improve the efficiency of its radiology department and its responsiveness to doctors’ needs. Administrators have observed that, every hour, doctors submit an average of 18 X-ray films for examination by staff radiologists. Each radiologist is equipped with a conventional piece of viewing equipment that reads one film at a time. Because of complications that vary from case to case, the actual time needed for report preparation is exponentially distributed with a mean of 30 minutes. Together, the cost of leasing one piece of viewing equipment and each radiologist’s salary is $ 100 per hour. Although it is difficult to put a dollar value on a doctor’s waiting time, each doctor would like to get a radiologist’s report within an average of 40 minutes from the time the film is submitted.

a. Determine the number of radiologists that the hospital should staff in order to meet doctors’ requirements regarding job flow time. Compute the resulting hourly cost of operating the radiology department.

b. The hospital could also change its diagnostic procedure by leasing more sophisticated X- ray viewing devices. Administrators estimate that the new procedure would reduce a radiologist’s average film- processing time to 20 minutes. At the same time, however, higher equipment rental and salaries for additional support personnel would boost the hourly cost per radiologist to $ 150. Determine the number of radiologists that the hospital should staff under this new arrangement. Would the new arrangement be economically advantageous?