Baton Rouge's Mt. Cedar Hospital is a large, private, 600-bed facility complete with laboratories, operating rooms, and X-ray equipment. In seeking to increase revenues, Mt. Cedar'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 generates $1,515 in revenues. The laboratory is capable of handling 14,500 tests per year more than it was handling. The average 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 7,200 X-rays without significant additional cost. Finally, the administration estimates that up to

2,700 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.

Develop LP model and using graphical solution, determine the optimal solution.

Decision variables: X1 = number of medical patients

X2 = number of surgical patients

Transcribed Image Text:variables. X₁ = number of medical patients X₂ = number of surgical patients Aim of the objective function should be Objective Value Z = Subject to: expected revenue as a result of expansion (patient days available) - C₁ (lab tests) - C₂ (X rays) - C3 (surgeries) - C4 X₁, X₂ ≥0 Constraints, C₁, C₂, C3, and C4 using the line graphing tool have been plotted on the graph provided on right. Using the point drawing tool, locate all the corner points for the feasible area on the graph. The optimum solution is: X₁ = X₂ = (round your response to two decimal places). (round your response to two decimal places). Optimal solution value Z = (round your response to two decimal places). % of beds to be assigned to medical patients = % of beds to be assigned to surgical patients = % (round your response to one decimal place). % (round your response to one decimal place). Out of the given 90 beds, medical patients should get beds (round your response to the nearest whole number). Surgical patients should get beds (round your response to the nearest whole number).

Question

Baton​ Rouge's Mt. Cedar Hospital is a​ large, private,​ 600-bed facility complete with​ laboratories, operating​ rooms, and​ X-ray equipment. In seeking to increase​ revenues, Mt.​ Cedar'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 $2,280in revenues. The average surgical patient is in the hospital 5 days and generates $1,515 in revenues. The laboratory is capable of handling 14,500 tests per year more than it was handling. The average medical patient requires 3.1 lab​ tests, the average surgical patient 2.6 lab tests. ​ Furthermore, the average medical patient uses1 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 7,200 ​X-rays without significant additional cost. ​ Finally, the administration estimates that up to2,700 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. Develop LP model and using graphical​ solution, determine the optimal solution. Decision​ variables: X1 ​= number of medical patientsX2 ​= number of surgical patients variables.X₁ = number of medical patientsX₂ = number of surgical patientsAim of the objective function should beObjective Value Z =Subject to:expected revenue as a result of expansion(patient days available) - C₁(lab tests) - C₂(X rays) - C3(surgeries) - C4X₁, X₂ ≥0Constraints, C₁, C₂, C3, and C4 using the line graphing tool have been plotted on the graph provided on right.Using the point drawing tool, locate all the corner points for the feasible area on the graph.The optimum solution is:X₁ =X₂ =(round your response to two decimal places).(round your response to two decimal places).Optimal solution value Z = (round your response to two decimal places).% of beds to be assigned to medical patients =% of beds to be assigned to surgical patients =% (round your response to one decimal place).% (round your response to one decimal place).Out of the given 90 beds, medical patients should get beds (round your response to the nearest wholenumber).Surgical patients should get beds (round your response to the nearest whole number).

Accepted Answer

Based on the given information, the decision variables are X1 and X2. 
Here, the revenue details are…