Salt Lake County Hospital is assessing its Emergency Departm

Salt Lake County Hospital is assessing its Emergency Department (ED) capacity so it knows how to expand as the country population grows. The hospital has the following information about the ED:

on average, nurses need to spend 35 minutes with each patient that comes in. Additionally, physicians need to spend an average of 19 minutes with each patient. Each technician can X-ray up to 5 patients per hour. All patients have to go through one nurse, one physician and the x-ray.

1. what is the total capacity of nurses, as in the maximum number of patients the nurses can see in one hour? Round your answer to 1 decimal place.

2. what is the total capacity of physicians, as in the maximum number of patients physicians can see in one hour? round your answer to 1 decimal place.

3. what is the total capacity of x-ray techinicians, as in the maximum number of patients physicians can see in one hour? round your answer to 1 decimal place.

4. what is the total capacity of the x-ray techinicians (max # of patients that can be x-rayed in one hour)? round your answer to 1 decimal place.

Solution

To be calculated:

a) Total capacity of nurses

b) Total capacity of physicians

c) Total capacity of x-ray technicians

Given values:

a) Time nurses spend with each patient = 35 minutes

Total number of nurses = 12

b) Time physicians spend with each patient = 19 minutes

Total number of physicians = 5

c) Number of patients a technician X-ray = 5 patients per hour

  Total number of X-ray technicians = 4

Solution:

1) Total capacity of nurses, i.e. maximum number of patients the nurses can see in one hour can be calculated as;

Time nurses spend with each patient = 35 minutes

Number of patients one nurse can see in 1 min. = 1/35 patients

Number of patients one nurse can see in 60 mins. (1 hour) = 60/35 = 1.71 patients

Number of patients 12 nurses can see in 60 mins. (1 hour) = 1.71 x 12 = 20.5 patients

Total capacity of nurses = 20.5 patients

2) Total capacity of physicians, i.e. maximum number of patients the physicians can see in one hour can be calculated as;

Time physicians spend with each patient = 19 minutes

Number of patients one physician can see in 1 min. = 1/19 patients

Number of patients one physician can see in 60 mins. (1 hour) = 60/19 = 3.16 patients

Number of patients 5 physicians can see in 60 mins. (1 hour) = 3.16 x 5 = 15.8 patients

Total capacity of physicians = 15.8 patients

3) Total capacity of x-ray technicians, as in the maximum number of patients that can be x-rayed in one hour can be calculated as;

1 technician X-ray = 5 patients per hour

4 technician X-ray = 5 x 4 = 20 patients per hour

Total capacity of X-ray technicians = 20 patients