Answer
Using Jefferson's method, each shift is apportioned the following number of nurses:
Shift A is apportioned 57 nurses.
Shift B is apportioned 81 nurses.
Shift C is apportioned 68 nurses.
Shift D is apportioned 44 nurses.
Work Step by Step
We can find the total number of patients.
total patients = 453 + 650 + 547 + 350
total patients = 2000
We can find the standard divisor.
$standard~divisor = \frac{total ~patients}{number~of~ nurses}$
$standard~divisor = \frac{2000}{250}$
$standard~divisor = 8$
We can find each shift's standard quota. The standard quota of each shift is the number of patients during the shift divided by the standard divisor.
Shift A:
$standard ~quota = \frac{patients}{standard~divisor}$
$standard~quota = \frac{453}{8}$
$standard~quota = 56.63$
Shift B:
$standard ~quota = \frac{patients}{standard~divisor}$
$standard~quota = \frac{650}{8}$
$standard~quota = 81.25$
Shift C:
$standard ~quota = \frac{patients}{standard~divisor}$
$standard~quota = \frac{547}{8}$
$standard~quota = 68.38$
Shift D:
$standard ~quota = \frac{patients}{standard~divisor}$
$standard~quota = \frac{350}{8}$
$standard~quota = 43.75$
If each shift is apportioned its lower quota, the number of nurses apportioned is 56 + 81 + 68 + 43 which is 248 nurses. Since there is a total of 250 nurses available, there are two surplus nurses. To obtain a sum of 250 nurses, we need to find a modified divisor that is slightly less than the standard divisor.
Let's choose a modified divisor of 7.94. 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 shift.
Shift A:
$ modified ~quota = \frac{patients}{modified~divisor}$
$ modified ~quota = \frac{453}{7.94}$
$ modified ~quota = 57.05$
Shift B:
$ modified ~quota = \frac{patients}{modified ~divisor}$
$modified ~quota = \frac{650}{7.94}$
$modified ~quota = 81.86$
Shift C:
$modified ~quota = \frac{patients}{modified ~divisor}$
$modified ~quota = \frac{547}{7.94}$
$modified ~quota = 68.89$
Shift D:
$modified ~quota = \frac{patients}{modified ~divisor}$
$modified ~quota = \frac{350}{7.94}$
$modified ~quota = 44.08$
Using Jefferson's method, each shift is apportioned the lower quota of the modified quota. Each shift is apportioned the following number of nurses:
Shift A is apportioned 57 nurses.
Shift B is apportioned 81 nurses.
Shift C is apportioned 68 nurses.
Shift D is apportioned 44 nurses.
Note that the total number of nurses apportioned is 250, so using a modified divisor of 7.94 is acceptable.