Answer
Using Webster'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 the standard quota for each shift is rounded to the nearest whole number, the number of nurses apportioned is 57 + 81 + 68 + 44 which is 250 nurses. Since this is the correct number of nurses, we can use the standard divisor to apply Webster's method.
Using Webster's method, the quota for each shift is rounded to the nearest whole number. 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 divisor of 8 is acceptable.
