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Chapter 13: Problem 6

A university is composed of five schools. The enrollment in each school is given in the following table. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { School } & \begin{array}{c} \text { Liberal } \\ \text { Arts } \end{array} & \begin{array}{c} \text { Educa- } \\ \text { tion } \end{array} & \text { Business } & \begin{array}{c} \text { Engi- } \\ \text { neering } \end{array} & \text { Sciences } \\ \hline \text { Enrollment } & 1180 & 1290 & 2140 & 2930 & 3320 \\ \hline \end{array} $$ There are 300 new computers to be apportioned among the five schools according to their respective enrollments. Use Hamilton's method to find each school's apportionment of computers.

Short Answer

Expert verified
The apportionment of computers is as follows: Liberal Arts will receive 33 computers, Education will receive 36 computers, Business will receive 59 computers, Engineering will receive 81 computers and Sciences will receive 91 computers.

Step by step solution

01

Calculate Total Enrollment

The total enrollment can be found by adding up the enrollments of all the schools. So, add 1180, 1290, 2140, 2930, and 3320 which gives a total enrollment of 10860.
02

Calculate Quotas

Hamilton's method first determines the standard divisor, which is the quotient of the total quantity of what is to be apportioned and the total number of apportionments. In this case, divide the total number of computers (300) by the total enrollment (10860). This gives a standard divisor of approximately 0.0276. Then, to find each school's quota, multiply the standard divisor by the enrollment of each school. Round down each of these quotas to the nearest whole number
03

Check and Adjust Apportionment if necessary

Add up the quotas calculated in the previous step. If it is less than the total number of computers, allocate the remaining computers to the entities which have the highest fractional parts in their quotas, one by one, until no computers are left. However, in this case, the sum of the quotas equates to the total number of computers (300), hence no adjustment is needed.
04

Finalize Apportionment

The final computer apportionment for each school will be the quotas calculated in Step 2, no further adjustment needed in this case.

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Most popular questions from this chapter

Describe the Borda count method. Is it possible to use this method without ranking the candidates? Explain.

A small country has 24 seats in the congress, divided among the three states according to their respective populations. The table shows each state鈥檚 population, in thousands, before and after the country鈥檚 population increase. $$ \begin{array}{|l|c|c|c|c|} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { Total } \\ \hline \begin{array}{l} \text { Original Population } \\ \text { (in thousands) } \end{array} & 530 & 990 & 2240 & 3760 \\ \hline \begin{array}{l} \text { New Population (in } \\ \text { thousands) } \end{array} & 680 & 1250 & 2570 & 4500 \\ \hline \end{array} $$ a. Use Hamilton鈥檚 method to apportion the 24 congressional seats using the original population. b. Find the percent increase, to the nearest tenth of a percent, in the population of each state. c. Use Hamilton鈥檚 method to apportion the 24 congressional seats using the new population. Does the population paradox occur? Explain your answer.

Research and present a group report on a brief history of apportionment in the United States.

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