Hospital ABC has opened a new satellite office in the North and wants to determine how many clinics that they should hold there per week for three specialties: ENT, Ortho, and Cardiology. Each specialty makes a certain amount of money per clinic and they want to maximize their profits in the new location. They have studied the weekly demand for patients from the area and the number of rooms and nurses needed for each clinic and it is provided below.

They have engaged the analytic department to determine the number of each type of clinic that they should schedule each week to maximize the profits. The analysts have determined that they need to develop an optimization model to answer the question.

The hospital has outline the following information regarding the clinic expansion

• Each ENT clinic brings in a profit of $1000. In each clinic, the ENT physicians can see 40 patients, and they need 4 rooms for the clinic and 2 nurses. There is a weekly demand of 100 patients for ENT.
• Each Ortho clinic brings in a profit of $1500. In each clinic the Ortho physicians can see 20 patients, and they need 6 rooms for the clinic and 3 nurses. There is a weekly demand of 80 patients for Ortho.
• Each Cardiology clinic brings in a profit of $2000. In each clinic the Ortho physicians can see 30 patients, and they need 8 rooms for the clinic and 4 nurses. There is a weekly demand of 125 patients for Ortho.
• There are 80 rooms available per week and 30 nurses.

If our decision variables are to determine the number of each type of clinic to offer, what is the objective function for the optimization model?

Let E = number of ENT Clinics to schedule

Let O = number of Ortho Clinics to schedule

Let C = number of Cariology Clinics to schedule

A. Max $1000*E + $1500*O + $2000*C

B. Min 4*E + 6*O + 8*C

C. Max 40*E + 20*O + 30*C

D. Min 2*E + 3*O + 8*C