Flaws of Apportionment Methods 1. In the year 2001, the economics department of a university had 25 teaching assistants (TAS) to be divided among three courses, according to their respective enrollments. Table 1 shows the courses and the standard quotas as calculated for 25 TAs and 26 TAs. Table 2 shows the same data for year 2002, when the enrollment levels were different. Table 1 (2001) Course General Economics Economics Theory Business Economics Standard quota with 25 TAs 13.26 7.34 4.41 Standard quota with 26 TAs 13.79 7.68 4.58 Table 2 (2002) Course General Economics Economics Theory Business Economics Standard quota with 25 TAS 13.39 7.57 4.63 Standard quota with 26 TAS 13.42 7.63 4.71 Use Hamilton's method to determine if the Alabama paradox occurs. If so, when? 2. A national business has a small West Coast regional office responsible for 1,059 customers and a larger East Coast regional office responsible for 9,041 customers. The table shows the number of customers handled by each regional office. Regional office West Coast East Coast Total Customers 1,059 9,041 10,100 The national sales managers makes 100 visits total each year to the regional offices, apportioned between the two offices with respect to the number of customers for which each is responsible. Suppose that a new St. Louis regional office is opened with 510 brand new customers, resulting in a distribution shown in the following table. Regional office West Coast East Coast St. Louis Total Customers 1,059 9,041 510 10,610The sales manager adds 5 additional annual visits to his schedule for the St. Louis regional office. Use Hamilton's method to apportion the sales manager's visits for when there were two regional offices and for when there were three regional offices. Then decide which, if either, of the following statements is true. I. The new states paradox occurs with respect to the sales manager's visits, when the third regional office is added. II. When the third regional office is added, the West Coast office will get one fewer visit from the sales manager than before.