Thinking Mathematically (6th Edition)

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

Chapter 13 - Voting and Apportionment - Chapter Summary, Review, and Test - Review Exercises: 33

Answer

Using Hamilton's method, each clinic is apportioned the following number of doctors: Clinic A is apportioned 6 doctors. Clinic B is apportioned 8 doctors. Clinic C is apportioned 12 doctors. Clinic D is apportioned 14 doctors.

Work Step by Step

We can find the total patient load. total load = 275 + 392 + 611 + 724 = 2002 We can find the standard divisor. $standard~divisor = \frac{total~load}{number~of~ doctors}$ $standard~divisor = \frac{2002}{40}$ $standard~divisor = 50.05$ The standard divisor is 50.05 We can find the standard quota for each clinic. Clinic A: $standard~quota = \frac{patient~load}{standard~divisor}$ $standard~quota = \frac{275}{50.05}$ $standard~quota = 5.49$ Clinic B: $standard~quota = \frac{patient~load}{standard~divisor}$ $standard~quota = \frac{392}{50.05}$ $standard~quota = 7.83$ Clinic C: $standard~quota = \frac{patient~load}{standard~divisor}$ $standard~quota = \frac{611}{50.05}$ $standard~quota = 12.21$ Clinic D: $standard~quota = \frac{patient~load}{standard~divisor}$ $standard~quota = \frac{724}{50.05}$ $standard~quota = 14.47$ Hamilton's method is an apportionment method that involves rounding each standard quota down to the nearest whole number. Surplus doctors are given, one at a time, to the clinics with the largest decimal parts in their standard quotas until there are no more surplus doctors. Initially, each clinic is apportioned its lower quota. Clinic A is apportioned 5 doctors. Clinic B is apportioned 7 doctors. Clinic C is apportioned 12 doctors. Clinic D is apportioned 14 doctors. The total number of doctors which have been apportioned is 5 + 7 + 12 + 14 = 38 doctors Since there is a total of 40 doctors, there are two surplus doctors. The first doctor is given to Clinic B because it has the largest decimal part (0.83) in its standard quota. The second doctor is given to Clinic A because it has the second largest decimal part (0.49) in its standard quota. Using Hamilton's method, each clinic is apportioned the following number of doctors: Clinic A is apportioned 5 + 1 = 6 doctors. Clinic B is apportioned 7 + 1 = 8 doctors. Clinic C is apportioned 12 doctors. Clinic D is apportioned 14 doctors.
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