EXAMPLE 4 The High School Teacher’s Dilemma

Let us use the Hamilton method to determine how many sections of geometry, precalculus, and calculus the high school teacher in Example 2 (page 577) should teach. Table 14.3 (page 577) displays the quotas for the three subjects,. 2.60, 1.65, and 0.75, respectively. Table 14.4 shows how to obtain the apportionment by the Hamilton method.

The lower quotas are the tentative apportionments, and their sum is 3, leaving two sections still to be apportioned. These go to precalculus and calculus, because the quotas for these courses have the largest fractional parts, 0.65 and 0.75, respectively.