Math 103,
Spring 2011, Solutions to Chapter 4A homework
8 points
4.
The “states” in any apportionment problem are the entities that will have “seats” assigned to them according to a
share rule. In this case, the states are the 4 shifts and the seats are the 225 nurses.
(a)
The standard divisor
equals the total population divided by the number of seats, i.e. the total number of patients
divided by the number of nurses, which
871 + 1029 + 610 + 190
12
225
=
=
(b) The standard divisor represents the
average
number of patients per nurse
.
Another way to phrase this is
that if every nurse cared for exactly the same number of patients, that number of patients would be 12.
(c)
A
has standard quota
871
72.583
12
=
;
B
has standard quota
1029
85.75
12
=
;
C
has standard quota
610
50.833
12
=
;
D
:
190
15.833
12
=
6 points
14.
Applying Hamilton's method leads to the following results:
Shift
Standard
quota
Lower
standard
quota
Fractional
part
Hamilton
apportionment
(number of nurses)
A
72.583
72
.583
72
B
85.75
85
.75
86
C
50.833
50
.833
51
D
15.833
15
.833
16
Total:
225
222
3
225
The last column indicates how many nurses are apportioned to each shift under Hamilton's method.
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 Spring '07
 Berkowitz
 Math, Division, Fraction, Divisor, Quota

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