   # Building Inspectors A city apportions 34 building inspectors among three regions according to their populations. The following table shows the present population of each region. a. Use the Hamilton method to apportion the inspectors. b. After a year the regions have the following populations. Region A has an increase in population of 442, which is an increase of 3.03%. Region B has an increase in population of 103, which is an increase of 3.10%. Region C has an increase in population of 121, which is an increase of 0.40%. If the inspectors are reapportioned using the Hamilton method, will the population paradox occur? Explain. ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4, Problem 8RE
Textbook Problem
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## Building Inspectors A city apportions 34 building inspectors among three regions according to their populations. The following table shows the present population of each region. a. Use the Hamilton method to apportion the inspectors.b. After a year the regions have the following populations. Region A has an increase in population of 442, which is an increase of 3.03%. Region B has an increase in population of 103, which is an increase of 3.10%. Region C has an increase in population of 121, which is an increase of 0.40%. If the inspectors are reapportioned using the Hamilton method, will the population paradox occur? Explain.

To determine

(a)

Use the Hamilton method to apportion the inspectors.

### Explanation of Solution

Given Information:

 Office Los Angeles Newark Employees 1430 235

Concept used:

Standard Divisor=Total Population Number of city to apportion

Calculation:

Since, a city apportions 34 building inspectors among three regions first we calculate standard divisor.

Standard Divisor=Total Population Number of city to apportion

Therefore,

Standard Divisor=14566+3321+2998834=47875341408.08

Now in Hamilton method divide each enrollment by standard divisor to get a quotient and standard quota

 Region Population Quotient Standard quota Number of city to apportion A 14566 145661408
To determine

(b)

If the inspectors are reapportioned using the Hamilton method, will the population paradox occur? Explain.

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