New Orleans's Mt. Sinai Hospital is a large, private, 600-bed facility complete with laboratories, operating rooms, and X-ray equipment. In seeking to increase revenues, Mt. Sinai'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 $2,280 in net revenue. The average surgical patient is in the hospital 5 days and generates $1,515 in net revenue. The laboratory is capable of handling 15,000 tests per year more than it was handling. The avenge medical patient requires 3.1 lab tests, the average surgical patient 2.6 lab tests. Furthermore, the average medical patient uses 1 X ray, the average surgical patient 2 X rays. if the hospital were expanded by 90 beds, the X-ray department could handle up to 7,000 X rays without significant additional cost. Finally, the administration estimates that up to 2,800 additional operations could be performed in existing operating-room facilities. Assume medical patients require no surgery, whereas each surgical patient has an average of one surgery performed.
Formulate this problem so as to determine how many medical beds and how many surgical beds should be added in order to maximize revenues. Assume that the hospital is open 365 days per year.