Answer
Using Jefferson's method, the doctors are apportioned to the clinics as follows:
Clinic A is apportioned 7 doctors.
Clinic B is apportioned 15 doctors.
Clinic C is apportioned 9 doctors.
Clinic D is apportioned 17 doctors.
Clinic E is apportioned 10 doctors.
Clinic F is apportioned 12 doctors.
Work Step by Step
We can find the total patient load.
total load = 316 + 598 + 396 + 692 + 426 + 486
total load = 2914
We can find the standard divisor.
$standard ~divisor = \frac{total ~patient~load}{doctors}$
$standard ~divisor = \frac{2914}{70}$
$standard ~divisor = 41.63$
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 less than 70 doctors. To obtain a sum of 70 doctors, we need to find a modified divisor that is slightly less than the standard divisor.
Using the hint in the question, let's choose a modified divisor of 39.7. Note that it may require a bit of trial-and-error to find a modified divisor that works. We can find the modified quota for each clinic.
Clinic A:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{316}{39.7}$
$modified~quota = 7.96$
Clinic B:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{598}{39.7}$
$modified~quota = 15.06$
Clinic C:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{396}{39.7}$
$modified~quota = 9.97$
Clinic D:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{692}{39.7}$
$modified~quota = 17.43$
Clinic E:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{426}{39.7}$
$modified~quota = 10.73$
Clinic F:
$modified~quota = \frac{patient~load}{modified~divisor}$
$modified~quota = \frac{486}{39.7}$
$modified~quota = 12.24$
Using Jefferson's method, we apportion the doctors by rounding the modified quota down to the nearest whole number. The doctors are apportioned to the clinics as follows:
Clinic A is apportioned 7 doctors.
Clinic B is apportioned 15 doctors.
Clinic C is apportioned 9 doctors.
Clinic D is apportioned 17 doctors.
Clinic E is apportioned 10 doctors.
Clinic F is apportioned 12 doctors.
Note that the sum of the apportioned doctors is 70 doctors, so using 39.7 as a modified divisor is acceptable.
