   # 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. ### 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 4.1, 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.  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 Quotient Standard quota Number of Projectors A 840 840215.92≈3.890 3 4 B 1936 1936215.92≈8.966 8 9 C 310 310215.92≈1.435 1 1 D 2744 2744215.92≈12.708 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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