Explanation Packard-Hue manufactures testing equipment at four locations, and had just hired 300 new employees. Those employees are to be apportioned using production levels at the four locations according to Jefferson’s plan. The locations and production are as follows: Locations Production Atlanta 12 , 520 Buffalo 4 , 555 Carson City 812 Denver 947 Formula used: STANDARD DIVISOR = TOTAL POPULATION NUMBER OF SHARES STANDARD QUOTA = TOTAL POPULATION STANDARD DIVISOR In Jefferson’s plan, use the following steps: Step-1: Calculate the standard quota ( q ) using standard devisor ( d ) for each district. Step-2: Round the standard quotas down to get lower quotas and these quotas together to find the total number of representatives. It will either be correct, or it will be too small. Step-3: If it is small, lower the standard divisor in small increments to find a modified divisor that will give modified quotas that provide the appropriate total. The total production is 12 , 520 + 4 , 555 + 812 + 947 = 18 , 834 . The number of employees is 300 . Substitute the values of the total production and number of employees in the formula of the standard divisor d , d = 18 , 834 300 = 62.78 Therefore, the standard divisor is 62.78 . Substitute the values of production for each location and standard divisor d in the formula of standard quota. The values of standard quota and lower quota are summarized in the below table, Locations Standard Quota ( q ) Lower quota Atlanta 12 , 520 62.78 = 199.42660 ≈ 199.43 199 Buffalo 4 , 555 62.78 = 72.55495 ≈ 72.55 72 Carson City 812 62.78 = 12.93406 ≈ 12.93 12 Denver 947 62.78 = 15.08442 ≈ 15.08 15 Add these lower quotas together: 199 + 72 + 12 + 15 = 298 . Lower quotas total is 298 but the number of representatives is 300 , therefore lower the standard divisor d = 62

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 17.4, Problem 40PS

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The modified divisor that will produce the appropriate modified quotas totaling the 300 new employees. Those employees are to be apportioned using production levels at the four locations according to Jefferson’s plan.

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Chapter 17.4, Problem 39PS

Chapter 17.4, Problem 41PS

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Nature of Mathematics (MindTap Course List)

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The modified divisor that will produce the appropriate modified quotas totaling the 300 new employees. Those employees are to be apportioned using production levels at the four locations according to Jefferson’s plan.

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The modified divisor that will produce the appropriate modified quotas totaling the 300 new employees. Those employees are to be apportioned using production levels at the four locations according to Jefferson’s plan.

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Chapter 17 Solutions