952 CHAPTER 14 Voting and Apportionment 12. Forklifts Granite Manufacturing has 100 forklifts to apportion among three factories. The forklifts are to be apportioned based on the number of employees at each factory as shown in the table below. Factory A B C Total Employees 3822 7818 28,360 40,000 a) Apportion the forklifts using Hamilton’s method. 10, 19, 71 b) Suppose that 1 year later the factories have the following number of employees. If the 100 forklifts are reapportioned to the factories, does the population paradox occur using Hamilton’s method? Yes, factory A loses a forklift to factory B even though the population of factory A increased faster than the population of factory B. Factory A B C Total Employees 3861 7896 28,360 40,117 13. 3-D Printers A college with five divisions has funds for 54 3-D printers. The student population for each division is shown in the table below. Division A B C D E Total Population 733 1538 933 1133 1063 5400 a) Apportion the printers using Hamilton’s method. 7, 16, 9, 11, 11 b) Suppose that 1 year later the divisions have the following populations. If the college wishes to apportion 54 printers, does the population paradox occur using Hamilton’s method? * Division A B C D ETotal Population 733 1539 933 1133 1116 5454 14. Legislative Seats A country with three states has 250 seats in the legislature. The population of each state is shown in the following table. Dmitry Kalinovsky/Shutterstock State A B C Total Population 459 10,551 18,990 30,000 a) Apportion the seats using Hamilton’s method. 4, 88, 158 b) Suppose that in 10 years the states have the following populations. If the country reapportions 250 seats in the legislature, does the population paradox occur using Hamilton’s method? No State A B C Total Population 464 10,551 19,100 30,115 15. Additional Employees Scalene Technologies has employees in Europe, labeled A, and in the United States, labeled B. The number of employees in each group is shown in the table below. There are 48 managers to be apportioned between the two groups. Scalene Technologies A B Total Employees 844 3956 4800 a) Apportion the managers using Hamilton’s method. 8, 40 b) Suppose that additional employees in Asia, labeled C, with the number of employees shown in the table below, are added with seven new managers. Does the new-states paradox occur using Hamilton’s method? * Scalene Technologies A B C Total Employees 844 3956 724 5524 16. Adding a Park The town of Fallsview purchased 25 new picnic tables to be apportioned between two parks. The picnic tables are to be apportioned based on the annual number of visitors to each park as shown below. Park A B Total Visitors 3750 6250 10,000 a) Apportion the picnic tables using Hamilton’s method. 9, 16 b) Suppose that the town decides to purchase five additional picnic tables and include a third park with an annual number of visitors as shown in the table below. The town will now apportion 30 picnic tables among the three parks. Does the new-states paradox occur using Hamilton’s method? No. The apportionment is 9, 16, 5. Park A B C Total Visitors 3750 6250 2100 12,100 17. Adding a State A country with two states has 33 seats in the legislature. The population of each state is shown in the table below. State A B Total Population 744 2556 3300 *See Instructor Answer Appendix lucadp/Shutterstock
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