#### Answer

Using Jefferson's method, the doctors are apportioned to the clinics as follows:
Clinic A is apportioned 17 doctors.
Clinic B is apportioned 55 doctors.
Clinic C is apportioned 24 doctors.
Clinic D is apportioned 54 doctors.

#### Work Step by Step

We can find the total patient load.
total load = 1714 + 5460 + 2440 + 5386 = 15,000
We can find the standard divisor.
$standard ~divisor = \frac{total ~patient~load}{doctors}$
$standard ~divisor = \frac{15,000}{150}$
$standard ~divisor = 100$
If we use the standard divisor and round each standard quota down to the nearest whole number, the sum of the apportioned doctors will be 17 + 54 + 24 + 53 which is 148 doctors. To obtain a sum of 150 doctors, we need to find a modified divisor that is slightly less than the standard divisor.
Let's choose a modified divisor of 99. We can find the modified quota for each clinic.
Clinic A:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{1714}{99}$
$modified~quota = 17.31$
Clinic B:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{5460}{99}$
$modified~quota = 55.15$
Clinic C:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{2440}{99}$
$modified~quota = 24.65$
Clinic D:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{5386}{99}$
$modified~quota = 54.40$
Using Jefferson's method, we need to apportion the doctors with the lower quota. The doctors are apportioned to the clinics as follows:
Clinic A is apportioned 17 doctors.
Clinic B is apportioned 55 doctors.
Clinic C is apportioned 24 doctors.
Clinic D is apportioned 54 doctors.
Note that the sum of the apportioned doctors is 150 doctors, so using 99 as a modified divisor is acceptable.