The city of Bloomington has 17 neighborhoods. The number of high school students in each neighborhood and the time required to drive from each neighborhood to each of the city’s two high schools (North and South) are listed in the file P09_09.xlsx. The Bloomington Board of Education needs to determine how to assign students to high schools. All students in a given neighborhood must be assigned to the same high school. The Board has set (in order of priority, from highest to lowest) the following goals:

■ Goal 1: Ensure that the difference in enrollment at the two high schools differs by at most 50.

■ Goal 2: Ensure that average student travel time is at most 13 minutes.

■ Goal 3: Ensure that at most 4% of the students must travel at least 25 minutes to school.

a. Determine an optimal assignment of students to high schools.

b. If the enrollment at the two high schools can differ by at most 100 (a change in goal 1), how does your answer change?