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Question Linear Programming help

A large private hospital in Nottingham is seeking to increase revenues by adding extra beds. It presently has 600 beds complete with laboratories, operating rooms and X-ray equipment. It now wants to make a 90-bed addition on a portion o adjacent land currently used for staff parking. The administrators feel that the labs, operating rooms, and X-ray department are not being fully utilised at present and do not need to be expanded to handle additional patients. The addition of 90 beds, however, involves deciding how many beds to be allocated to the medical staff for medical patients and how many to the surgical staff for surgical patients.

Some pertinent information is available from the hospital’s accounting and medical records departments.

• The average hospital stay or a medical patient is 8 days and the average medical patient generates £7140 amount in revenues. • The average surgical patient is in the hospital for 5 days and receives an amount of £4062 bill. • The laboratory is capable of handling 15,000 tests per year more than it has been 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 2 X-rays, whereas the average surgical patient requires 4 X-rays. • If the hospital was expanded by 90 beds, the X-ray department could handle up to 6214 number of 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, require no surgery whereas each surgical patient generally has one surgery performed.

Ignoring any other consideration, develop a linear programming model so as to determine how many medical beds and how many surgical beds should be added to maximise revenues. Assume that the hospital is open or 365 days a year.

vikki_roberts in Maths about 9 years ago

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