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: 9

Answer

Using Jefferson's method, the doctors are apportioned to the clinics as follows: Clinic A is apportioned 17 doctors. Clinic B is apportioned 55 doctors. Clinic C is apportioned 24 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 down to the nearest whole number, the sum of the apportioned doctors will be 17 + 54 + 24 + 53 which is 148 doctors. To obtain a sum of 150 doctors, we need to find a modified divisor that is slightly less than the standard divisor. Let's choose a modified divisor of 99. We can find the modified quota for each clinic. Clinic A: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{1714}{99}$ $modified~quota = 17.31$ Clinic B: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{5460}{99}$ $modified~quota = 55.15$ Clinic C: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{2440}{99}$ $modified~quota = 24.65$ Clinic D: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{5386}{99}$ $modified~quota = 54.40$ Using Jefferson's method, we need to apportion the doctors with the lower quota. The doctors are apportioned to the clinics as follows: Clinic A is apportioned 17 doctors. Clinic B is apportioned 55 doctors. Clinic C is apportioned 24 doctors. Clinic D is apportioned 54 doctors. Note that the sum of the apportioned doctors is 150 doctors, so using 99 as a modified divisor is acceptable.
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