Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 13 - Voting and Apportionment - 13.3 Apportionment Method - Exercise Set 13.3: 14

Answer

Using Adams's method, the doctors are apportioned to the clinics as follows: Clinic A is apportioned 17 doctors. Clinic B is apportioned 54 doctors. Clinic C is apportioned 25 doctors. Clinic D is apportioned 54 doctors.

Work Step by Step

We can find the total patient load. total load = 1714 + 5460 + 2440 + 5386 = 15,000 We can find the standard divisor. $standard ~divisor = \frac{total ~patient~load}{doctors}$ $standard ~divisor = \frac{15,000}{150}$ $standard ~divisor = 100$ If we use the standard divisor and round each standard quota up to the nearest whole number, the sum of the apportioned doctors will be 18 + 55 + 25 + 54 which is 152 doctors. To obtain a sum of 150 doctors, we need to find a modified divisor that is slightly more than the standard divisor. Let's choose a modified divisor of 101.2. Note that it may take some trial-and-error to find a modified divisor that works. We can find the modified quota for each clinic. Clinic A: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{1714}{101.2}$ $modified~quota = 16.94$ Clinic B: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{5460}{101.2}$ $modified~quota = 53.95$ Clinic C: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{2440}{101.2}$ $modified~quota = 24.11$ Clinic D: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{5386}{101.2}$ $modified~quota = 53.22$ Using Adams's method, we need to apportion the doctors rounding up the modified quota to the nearest whole number. The doctors are apportioned to the clinics as follows: Clinic A is apportioned 17 doctors. Clinic B is apportioned 54 doctors. Clinic C is apportioned 25 doctors. Clinic D is apportioned 54 doctors. Note that the sum of the apportioned doctors is 150 doctors, so using 101.2 as a modified divisor is acceptable.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.