# 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.

### Mathematical Excursions (MindTap C...

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

### Mathematical Excursions (MindTap C...

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

#### Solutions

Chapter 4, Problem 1RE
Textbook Problem

## 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.

Expert Solution
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 1280192.18≈6.660 6 Business 3425 3425192.18≈17.821 17 Engineering 1968 1968192.18≈10.240 10 Science 2936 2936192.18≈15.277 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 1280192.18≈6.660 6 7 Business 3425 3425192.18≈17.821 17 18 Engineering 1968 1968192.18≈10.240 10 10 Science 2936 2936192.18≈15.277 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.

Expert Solution
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 1280182.9≈6.998 6 Business 3425 3425182.9≈18.726 18 Engineering 1968 1968182.9≈10.726 10 Science 2936 2936182.9≈16.052 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

Expert Solution
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 1280192.18≈6.660 6 7 Business 3425 3425192.18≈17.821 17 18 Engineering 1968 1968192.18≈10.240 10 10 Science 2936 2936192.18≈15.277 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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