Question

Part 5 of 5 -

Part 5

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 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 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.

Assume that the hospital is open 365 days a year. Round off your answers to the nearest integer.

Question 9 of 11 10.0 Points The optimal number of medical patients per year is __________ , and optimal number of surgical patients per year is ____________ . The maximum annual profit is _________ dollars. (Please round to the closest integer and include no units.) Mark for Review What's This?

Question 10 of 11 10.0 Points Among the 90 additional beds, _______ beds should be used for medical patients and _______ beds used for surgical patients. A. 45, 45 B. 60, 30 C. 61, 29 D. 29, 61

Question 11 of 11 10.0 Points At the optimal, there are __________ empty beds, _________________ lab tests of unused capacity, ______________ x-rays of unused capacity, and _____________ unused operation rooms available. (Please round to the closest integer and include no units.)

Answer 1

Revenue per patient-day of medical patient=$2280/8=$285

Revenue per patient-day of surgical  patient=$1515/5=$303

Total patient-day available=90*365=32850

Since revenue per day for surgical patient is higher , the maximum capacity should be allocated to surgical patients.

Total additional surgeries possible=2800

Maximum Number of patient to be allocated to surgery=2800

Number of patient days=2800*5=14000

Number of Lab tests required for 2800 Surgical patients=2800*2.6=7280

Number of X rays required for 2800 Surgical patients=2800*2=5600

Balance capacity available in terms of patient days =32850-14000=18850

Number of Medical patients =18850/8=2356

Number of Lab tests required for 2356 Medical  patients=2356*3.1=7304

Number of X rays required for 2356 Medical patients=2356*1=2356

LAB TEST CONSTRAINT	15000
Number of test required for Surgical patients	7280
Number of test required for Medical patients	7304
Total Number of Lab test required	14584
X RAY CONSTRAINT	7000
Number of X ray required for Surgical patients	5600
Number of X ray required for Medical patients	2356
Total Number of X Rays required	7956

X Ray Constraint is not satisfied.

Number of X rays required should be reduced by (7956-7000)=956

This can be achieved by reduction of 956/2=478 Surgical patients or 956 Medical patients

Reduction of 478 Surgical patients will reduce revenue by 1515*478=$724,170

Reduction of 956 Medical patients will reduce revenue by 2280*956=$2,179,680

Hence we should reduce 478 Surgical Patients

Final Number of Surgical Patients =2800-478=2322

Final Number of Medical Patients =2356

X RAY CONSTRAINT	7000
Number of X ray required for Surgical patients(2322*2)	4644
Number of X ray required for Medical patients	2356
Total Number of X Rays required(4644+2356)	7000

Annual Profit =1515*2322+2280*2356=$8,889,510

Number of Patient days for Surgical Patients =2322*5=11610

Number of Patient days for Medical Patients =2356*8=18848

Number of average beds used by Surgical Patients =11610/365=32

Number of average beds used by Medical Patients =18848/365=52

The optimal number of medical patients per year is 2356 and optimal number of surgical patients per year is 2322 . The maximum annual profit is 8,889,510

dollars.

Among the 90 additional beds, 60 beds should be used for medical patients and 30 beds used for surgical patients.

Idle Capacity:

Number of patient days idle=32850-11610-18848=2392

Average Number of idle beds =2392/365=7

Idle Lab Test Capacity =15000-14584=416

Unused Operating Room Capacity =2800-2322=478

At the optimal, there are 7 empty beds, 416 lab tests of unused capacity, NIL x-rays of unused capacity, and 478 unused operation rooms available.