Chapter 4, Problem 1RE

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.

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:

  $\text{Standard Divisor}=\frac{\text{Number of enrollments}}{\text{Number of overhead projectors to apportion}}$

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,

  $\text{Standard Divisor}=\frac{\text{Number of enrollments}}{\text{Number of overhead projectors to apportion}}$

Therefore,

  $\begin{array}{c}\text{Standard Divisor}=\frac{9609}{50}\\ =192.18\end{array}$

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	$1280$	$\frac{1280}{192.18}\approx 6.660$   $$	$6$
Business	$3425$	$\frac{3425}{192.18}\approx 17.821$	$17$
Engineering	$1968$	$\frac{1968}{192.18}\approx 10.240$	$10$
Science	$2936$	$\frac{2936}{192.18}\approx 15.277$	$15$
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	$1280$	$\frac{1280}{192.18}\approx 6.660$   $$	$6$	$7$
Business	$3425$	$\frac{3425}{192.18}\approx 17.821$	$17$	$18$
Engineering	$1968$	$\frac{1968}{192.18}\approx 10.240$	$10$	$10$
Science	$2936$	$\frac{2936}{192.18}\approx 15.277$	$15$	$15$
	$48$	$50$

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 $7,18,10,15$.

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:

  $\text{Standard Divisor}=\frac{\text{Number of enrollments}}{\text{Number of overhead projectors to apportion}}$

Calculation:

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

Divisions	Enrollments	Quotient	Standard Quota
Health	$1280$	$\frac{1280}{182.9}\approx 6.998$   $$	$6$
Business	$3425$	$\frac{3425}{182.9}\approx 18.726$	$18$
Engineering	$1968$	$\frac{1968}{182.9}\approx 10.726$	$10$
Science	$2936$	$\frac{2936}{182.9}\approx 16.052$	$16$
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

  $6,18,10,16$

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	$1280$	$\frac{1280}{192.18}\approx 6.660$   $$	$6$	$7$
Business	$3425$	$\frac{3425}{192.18}\approx 17.821$	$17$	$18$
Engineering	$1968$	$\frac{1968}{192.18}\approx 10.240$	$10$	$10$
Science	$2936$	$\frac{2936}{192.18}\approx 15.277$	$15$	$15$
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 $7,18,10,15$.