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.

Q: Expert Answer

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 Given Information: Center A B C D E Number of sales personnel 31 108 70 329 49 Apportionment of 27 automobiles 2 5 3 15 2 Concept used: Standard Divisor = Number of Students Number 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 Students Number of teachers to apportion Therefore, Standard Divisor = 31 + 108 + 70 + 329 + 49 28 = 587 28 ≈ 20.96 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 28 automobiles A 31 31 20.96 ≈ 1.48 1 2 B 108 108 20.96 ≈ 5.15 5 5 C 70 70 20 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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Answer 1

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Mathematical Excursions (MindTap C...

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

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BuyFind

Mathematical Excursions (MindTap C...

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Solutions

Chapter

Section

Answer 3

Solutions

Chapter

Section

Answer 4

Chapter

Section

Answer 5

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 27 automobiles	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=58728≈20.96

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 28 automobiles
A	31	3120.96≈1.48	1	2
B	108	10820.96≈5.15	5	5
C	70	7020

Answer 6

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.

Mathematical Excursions (MindTap C...

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Mathematical Excursions (MindTap C...

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