Grand River Hospital in Kitchener, Ontario, is a large, 600-bed facility complete with laboratories, operating rooms, and X-ray equipment. In seeking to optimize government funding, Grand River’s administration has decided to make a 90-bed addition on a portion of adjacent land currently used for staff parking. The administrators feel that the labs, operating rooms, and X-ray department are not being fully utilized at present and do not need to be expanded to handle additional patients. The addition of 90 beds, however, involves deciding how many beds should be allocated to the medical staff (for medical patients) and how many to the surgical staff (for surgical patients).
The hospital’s accounting and medical records departments have provided the following pertinent information. The average hospital stay for a medical patient is 8 days, and the average medical patient generates $2280 in funding. The average surgical patient is in the hospital five days and generates $1515 in funding. The laboratory is capable of handling 15 000 tests per year more than it was handling. The average medical patient requires 3.1 lab tests, the average surgical patient 2.6 lab tests. Furthermore, the average medical patient uses one X-ray, the average surgical patient two X-rays. If the hospital were expanded by 90 beds, the X-ray department could handle up to 7000 X-rays without significant additional cost. Finally, the administration estimates that up to 2800 additional operations could be performed in existing operating-room facilities. Medical patients, of course, require no surgery, whereas each surgical patient generally has one surgery performed.
Formulate this problem so as to determine how many medical beds and how many surgical beds should be added to maximize revenues. Assume that the hospital is open 365 days per year.