   # Automobile Sales Consider the apportionment of 27 automobiles to the sales departments of a business with five regional centers labeled A, B, C, D, and E. The following table shows the Hamilton apportionment of the automobiles based on the number of sales personnel at each center. a. If the number of automobiles to be apportioned increases from 27 to 28, what will be the apportionment if the Hamilton method is used? Will the Alabama paradox occur? Explain. b. If the number of automobiles to be apportioned using the Hamilton method increases from 28 to 29, will the Alabama 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 6RE
Textbook Problem
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## Automobile Sales Consider the apportionment of 27 automobiles to the sales departments of a business with five regional centers labeled A, B, C, D, and E. The following table shows the Hamilton apportionment of the automobiles based on the number of sales personnel at each center. a. If the number of automobiles to be apportioned increases from 27 to 28, what will be the apportionment if the Hamilton method is used? Will the Alabama paradox occur? Explain.b. If the number of automobiles to be apportioned using the Hamilton method increases from 28 to 29, will the Alabama paradox occur? Explain.

To determine

(a)

To Explain:

If the number of automobiles to be apportioned increases from 27 to 28, what will be the apportionment if the Hamilton method is used? Will the Alabama paradox occur? Explain.

### Explanation of Solution

Given Information:

 Center A B C D E Number of sales personnel 31 108 70 329 49 Apportionment of   27automobiles 2 5 3 15 2

Concept used:

Standard Divisor=Number of StudentsNumber of teachers to apportion

Calculation:

The number of automobiles to be apportioned increases from 27 to 28, first calculate standard divisor

Standard Divisor=Number of StudentsNumber of teachers to apportion

Therefore,

Standard Divisor=31+108+70+329+4928=5872820.96

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

 Center Number of sales personnel Quotient Standard quota Apportionment of   28automobiles A 31 3120.96≈1.48 1 2 B 108 10820.96≈5.15 5 5 C 70 7020
To determine

(b)

To Explain:

If the number of automobiles to be apportioned using the Hamilton method increases from\ 28 to 29, will the Alabama paradox occur? Explain.

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