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Education The science division of a college consists of three departments: mathematics, Physics, and chemistry. The number of students enrolled in each department is shown in the following table. There are 19 clerical assistants to be apportioned among the departments. a. Use the Hamilton method to find each department’s apportionment of clerical assistants. b. The division opens a new computer science department with a student enrolment of 495. The division decides 10 have a total of 20 clerical assistants. If the clerical assistants are reapportioned using the Hamilton method, will the new states 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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BuyFindarrow_forward

Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.1, Problem 20ES
Textbook Problem
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Education The science division of a college consists of three departments: mathematics, Physics, and chemistry. The number of students enrolled in each department is shown in the following table. There are 19 clerical assistants to be apportioned among the departments.

Chapter 4.1, Problem 20ES, Education The science division of a college consists of three departments: mathematics, Physics, and

a. Use the Hamilton method to find each department’s apportionment of clerical assistants.

b. The division opens a new computer science department with a student enrolment of 495.

The division decides 10 have a total of 20 clerical assistants. If the clerical assistants are reapportioned using the Hamilton method, will the new states paradox occur? Explain.

To determine

(a)

Use the Hamilton method to find each department's apportionment of clerical assistants.

Explanation of Solution

Given Information:

Department Math Physics Chemistry
Student enrollment  4325  520  1165

Concept used:

  Standard Divisor=Total EnrollmentNumber of security personnel to apportion

Calculation:

Since there are 19 clerical assistants to be apportioned among the departments first we calculate standard divisor.

  Standard Divisor=Total EnrollmentNumber of security personnel to apportion

Therefore,

  Standard Divisor=4320+520+116520=601020=300.5

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

Department Student Enrollment Quotient Standard quota Number of Clerical Assistants
Math's   4325  4325300
To determine

(b)

The division opens a new computer science department with a student enrollment of 495 .The division decides to have a total of 20 clerical assistants. If the clerical assistants are reapportioned using the Hamilton method, will the new states paradox occur? Explain.

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Chapter 4 Solutions

Mathematical Excursions (MindTap Course List)
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