Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 47

In Problem, the school board determined that it does not want any of the schools to be overly crowded compared with the other schools. It would like to assign students from each district to each school so that enrollments are evenly balanced between the four schools. However, the school board is concerned that this might significantly increase travel time. Determine the number of students to be assigned from each district to each school such that school enrollments are evenly balanced. Does this new solution appear to significantly increase travel time per student
Problem
Bayville has built a new elementary school, increasing the town's total to four schools-Addison, Beeks, Canfield, and Daley. Each has a capacity of 400 students. The school board wants to assign children to schools so that their travel time by bus is as short as possible. The school board has partitioned the town into five districts conforming to population density-north, south, east, west, and central. The average bus travel time from each district to each school is shown as follows:
Determine the number of children that should be assigned from each district to each school to minimize total student travel time.