We are trying to help the MCSCC (Monroe County School Corporation) determine the appropriate high school district for each housing development in Bloomington. For each development, we are given the number of students, the mean family income, the percentage of minorities, and the distance to each high school (South and North). These data are listed in the file P05_65.xlsx. In assigning the students, MCSCC wants to minimize total distance traveled subject to the following constraints:

■ Each school must have at least 1500 students.

■ The mean family income must be at least $85,000 for students of each school.

■ Each school must have at least 10% minorities.

Determine an optimal assignment of students to schools. Then provide a one-paragraph summary of how the optimal solution changes as the required minority percentage varies from 5% to 11%.