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College Enrollment The following table shows the enrollment for each of the four divisions of a college. The four divisions are liberal arts, business, humanities, and science. There are 180 new computers that are to be apportioned among the divisions based on the enrollments. Total 15.809 a. What is the standard divisor for an apportionm ent of the computers? What is the meaning of the standard divisor in the context of this exercise? b. Use the Hamilton method to determine the number of computers to be apportioned to each division. c. If the computers are to be apportioned using the Jefferson method, explain why neither 86 nor 87 can be used as a modified standard divisor. Explain why 86.5 can be used as a modified standard divisor. d. Explain why the modified standard divisor - used in the Jefferson method cannot be larger than the standard divisor. e. Use the Jefferson method to determine the number of computers to be apportioned to each division. Is this apportionment in violation of the quota rule? f. How do the apportionment results produced using the Jefferson method compare with the results prod uced using the Hamilton method?
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Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Solutions
Chapter
Section
BuyFindarrow_forward
Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.1, Problem 10ES
Textbook Problem
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College Enrollment The following table shows the enrollment for each of the four divisions of a college. The four divisions are liberal arts, business, humanities, and science. There are 180 new computers that are to be apportioned among the divisions based on the enrollments.
Total 15.809
a. What is the standard divisor for an apportionm ent of the computers? What is the meaning of the standard divisor in the context of this exercise?
b. Use the Hamilton method to determine the number of computers to be apportioned to each division.
c. If the computers are to be apportioned using the Jefferson method, explain why neither 86 nor 87 can be used as a modified standard divisor. Explain why 86.5 can be used as a modified standard divisor.
d. Explain why the modified standard divisor - used in the Jefferson method cannot be larger than the standard divisor.
e. Use the Jefferson method to determine the number of computers to be apportioned to each division. Is this apportionment in violation of the quota rule?
f. How do the apportionment results produced using the Jefferson method compare with the results prod uced using the Hamilton method?
To determine
(a)
To find:
The standard divisor for an apportionment of the computers.
Explanation of Solution
Given information:
The given table shows the enrollment for each of the four division of a college. The four divisions are liberal arts, business, humanities and science. There are 180 new computers that are to be apportioned among the divisions based on the enrollments.
  
To determine
(b)
To find:
The number of computers to be apportioned to each division.
To determine
(c)
To state:
The modified standard divisor.
To determine
(d)
Using Jefferson method to find standard divisor
To determine
(e)
To find:
number of computers using jefferon method
To determine
(f)
To compare:
The method of Hamilton and Jefferon
Chapter 4 Solutions
Mathematical Excursions (MindTap Course List)
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addCh. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Give each state one representative. Use the...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Explain how to calculate the standard divisor of...Ch. 4.1 - Teacher Aides A total of 25 teacher aides are to...Ch. 4.1 - In the Hamilton apportionment method, explain how...Ch. 4.1 - What is quota rule?Ch. 4.1 - Governing Boards The following table shows how the...Ch. 4.1 - Forest Rangers The table below shows how the...
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Explain how the pairwise comparison voting...Ch. 4.2 - What does the Condorcet criterion say?Ch. 4.2 - Is there a best voting method? 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