(Hospital expansion problem) Mt. Sinai Hospital in New Orleans 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 build 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, requires a decision as to 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 revenues. The average surgical patient is in the hospital 5 days and receives a

$1,515 bill. 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 and the average surgical patient takes 2.6 lab tests.

Furthermore, the average medical patient uses one x-ray, whereas the average surgical patient requires two x-rays. If the hospital was 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. Medical patients, of course, do not require 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 a year. Then solve the problem.