MT Sinai Hospital is a 600 bed facility complete with operating rooms and x ray equipment. They have decided to make a 90 bed addition. The addition of 90 beds 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 average hospital stay for a medical patient is 8 days and in average generates $2280 in revenues. The average surgical patient is in the hospital 5 days and receives a $1515 bill. The laboratory is capable of handling 1500 tests per year more than what it is handling. The average medical patient requires 3.1 lab tests and the average surgical patient requires 2.6 labs. the average medical patient requires 1 x rays and the surgical patient requires 2 x rays. if the hospital expanded by 90 beds the x ray department could handle up to 7000 xrays without significant additional cost. The administration estimates that up to 2800 additional operations could be performed in existing operation room facilities. medical patients do not require surgery and surgery patients only require one surgery.

what is the optimal number of medical patients and surgical patients per year?
At optimal what is the number of unused operation rooms available?