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Education The following table shows the enrollments for the four divisions of a college. There are 50 new overhead projectors that are to be apportioned among the divisions based on the enrollments. a. Use the Hamilton method to determine the number of projectors to be apportioned to each division. b. Use the Jefferson method to determine the number of projectors to be apportioned to each division. c. Use the Webster method to determine the number of projectors to be apportioned to each division.

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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, Problem 1RE
Textbook Problem
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Education The following table shows the enrollments for the four divisions of a college. There are 50 new overhead projectors that are to be apportioned among the divisions based on the enrollments.

Chapter 4, Problem 1RE, Education The following table shows the enrollments for the four divisions of a college. There are

a. Use the Hamilton method to determine the number of projectors to be apportioned to each division.

b. Use the Jefferson method to determine the number of projectors to be apportioned to each division.

c. Use the Webster method to determine the number of projectors to be apportioned to each division.

To determine

(a)

Use the Hamilton method to determine tile number of projectors to be apportioned to each division.

Answer to Problem 1RE

Hence, the projectors to be apportioned each division Health, Business, Engineering, and Science is 7,18,10,15.

Explanation of Solution

Given Information:

Number of overhead projectors =50

Concept used:

  Standard Divisor=Number of enrollmentsNumber of overhead projectors to apportion

Calculation:

Since there is a total 50 new overhead projectors should be apportioned standard divisor is calculated by total number of enrollments divided by total number of new over head projectors that are to be apportioned, formula for standard divisor is,

  Standard Divisor=Number of enrollmentsNumber of overhead projectors to apportion

Therefore,

  Standard Divisor=960950=192.18

Under the Hamilton plan, divide the enrollments of each division by the standard divisor and round the quotient down to a whole number

Divisions Enrollments Quotient Standard Quota
Health   1280  1280192.186.660
  
  6
Business   3425  3425192.1817.821  17
Engineering  1968  1968192.1810.240  10
Science   2936  2936192.1815.277  15
Total  48

When this happen the Hamilton plan calls for revisiting the calculation of the quotients and assigning an additional representative to the divisions with the largest decimal remaindeí process is continued until the number of representatives equals the number required by divisions. For divisions we have.

Divisions Enrollments Quotient Standard Quota Number of overhead projectors
Health   1280  1280192.186.660
  
  6  7
Business   3425  3425192.1817.821  17  18
Engineering  1968  1968192.1810.240  10  10
Science   2936  2936192.1815.277  15  15
  48  50

Hence, the projectors to be apportioned each division Health, Business, Engineering, and Science is 7,18,10,15.

Conclusion:

Hence, the projectors to be apportioned each division Health, Business, Engineering, and Science is 7,18,10,15.

To determine

(b)

Use the Jefferson method to determine the number of projectors to be apportioned to each division.

Answer to Problem 1RE

The projectors to be apportioned each division Health, Business, Engineering, and Science is

  6,18,10,16

Explanation of Solution

Given Information:

Division Enrollment
Health   1280
  
Business  3425
Engineering   1968
Science  2936
Total   9609

Concept used:

  Standard Divisor=Number of enrollmentsNumber of overhead projectors to apportion

Calculation:

For Jefferson plan we consider modified standard divisor by trial and error is 182.9.

Divisions Enrollments Quotient Standard Quota
Health   1280  1280182.96.998
  
  6
Business   3425  3425182.918.726  18
Engineering  1968  1968182.910.726  10
Science   2936  2936182.916.052  16
Total  50

Hence, the projectors to be apportioned each division Health, Business, Engineering, and Science is 6,18,10,16

Conclusion:

The projectors to be apportioned each division Health, Business, Engineering, and Science is

  6,18,10,16

To determine

(c)

Use the Webster method to determine the number of projectors to be apportioned to each division.

Answer to Problem 1RE

The projectors to be apportioned each division Health, Business, Engineering, and

Science is 7,18,10,15.

Explanation of Solution

Given Information:

Webster method

Concept used:

Webster method includes Enrollment, Quotient and number of overhead projects.

Calculation:

Now use Webster method to determine the number of projectors to be apportioned therefore,

Divisions Enrollments Quotient Standard Quota Number of overhead projectors
Health   1280  1280192.186.660
  
  6  7
Business   3425  3425192.1817.821  17  18
Engineering  1968  1968192.1810.240  10  10
Science   2936  2936192.1815.277  15  15
Total  48  50

Hence, the projectors to be apportioned each division Health, Business, Engineering, and

Science is 7,18,10,15.

Conclusion:

The projectors to be apportioned each division Health, Business, Engineering, and

Science is 7,18,10,15.

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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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