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Apportionment of Projectors Consider the apportionment of 27 digital projectors for a school district with four campus locations labeled A. B. C and D. The following table shows the apportionment of the projectors using the Hamilton method. a. If the number of projectors 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 projectors to be apportioned using the Hamilton method increases from 28 to 29, will the Alabama paradox occur? Explain.

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Mathematical Excursions (MindTap C...

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

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Section
BuyFindarrow_forward

Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.1, Problem 16ES
Textbook Problem
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Apportionment of Projectors Consider the apportionment of 27 digital projectors for a school district with four campus locations labeled A. B. C and D. The following table shows the apportionment of the projectors using the Hamilton method.

Chapter 4.1, Problem 16ES, Apportionment of Projectors Consider the apportionment of 27 digital projectors for a school , example  1

Chapter 4.1, Problem 16ES, Apportionment of Projectors Consider the apportionment of 27 digital projectors for a school , example  2

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

To determine

(a)

If tile number of projectors 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:

Campus   A  B  C  D
Enrollment  840  1936  310  2744
Apportionment of
  27projectors
  4  9  1  13

Concept used:

Albama paradox will not occur as there is no loss of projectors and also total enrollment is same.

Calculation:

Since, 27 digital projectors for a school district first we calculate standard divisor.

  Standard Divisor=Number of StudentsNumber of teachers to apportion

Therefore,

  Standard Divisor=840+1936+310+274427=583027215.92

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

Campus Enrollment QuotientStandard quotaNumber of Projectors
  A  840  840215.923.890  3  4
  B  1936  1936215.928.966  8  9
  C  310  310215.921.435  1  1
  D  2744  2744215.9212.708  12  13
Total  24  27

As projectors increase from 27 to 28, therefore standard divisor is

  Standard Divisor=840+1936+310+274428=583028208

To determine

(b)

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

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Chapter 4 Solutions

Mathematical Excursions (MindTap Course List)
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Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. 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