#### Answer

Using Hamilton'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:
$standard ~quota = \frac{patients}{standard~divisor}$
$standard~quota = \frac{350}{8}$
$standard~quota = 43.75$
Hamilton's method is an apportionment method that involves rounding each standard quota down to the nearest whole number. Surplus nurses are given, one at a time, to the shifts with the largest fractional parts in their standard quotas until there are no more surplus nurses.
Initially, each shift is apportioned its lower quota.
Shift A is apportioned 56 nurses.
Shift B is apportioned 81 nurses.
Shift C is apportioned 68 nurses.
Shift D is apportioned 43 nurses.
We can find the total number of nurses which have been apportioned.
total = 56 + 81 + 68 + 43 = 248 nurses
Since there is a total of 250 nurses available, there are two surplus nurses. The first nurse is given to Shift D because it has the largest fractional part (0.75) in its standard quota. The second nurse is given to Shift A because it has the second largest fractional part (0.63) in its standard quota.
Using Hamilton's method, each shift is apportioned the following number of nurses:
Shift A is apportioned 56 + 1 = 57 nurses.
Shift B is apportioned 81 nurses.
Shift C is apportioned 68 nurses.
Shift D is apportioned 43 + 1 = 44 nurses.