Heavenly Mercy Hospital wants to improve the efficiency of its radiology department and its responsiveness to doctors needs. Administration have observedthat. 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 taht 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 quipment and each radiologist's salary is $100 per hour. Althoug it is difficult to put a dollar value on a doctor's waiting time, each doctor would like to get a daiologist's report within an average of 40 minutes from the time the film is submitted.
Show all work.
a. How many radiologist should the hospital hire? Compute the resulting hourly cost of of operating the radiology department.
The hospital could also change its diagnostic procedure by leasing more sophisticated X-ray devices: this would reduce a radiologist's average film-processing time to 20 minutes, but the rental and salaries would boost costs per radiologists to $150.
b. How many radiologist should the hospital hire? What is the resulting hourly cost of operating the radiology department? Would the new arrangement be advantageous?