Discussion:
Q: The Springdale School board has made the decision to close one its junior high schools (seventh and eight grades) at the end of the school year and reassign all of next year's students to one of the three remaining junior high schools. The school district for the closed school has been divided into five areas as shown in the table below. The number of students in each of the five areas attending junior high next year is indicated in the second column. The school district provides busing for all students who must travel more than a mile. Therefore the school board wants a plan for reassigning the students that will minimize the total busing cost. The annual cost per student for busing from each of the five residential areas of the city to each of the three remaining schools is also shown in the table below. A zero indicates that busing is not needed and a dash indicates an infeasible assignment (i.e. the student lives more than five miles from the school which violates a school board policy). The bottom of the table indicates the maximum number of students each of the three remaining schools will be able to accept. The students in a given area do not all have to be sent to the same school. (e.g., a third of the students in area 1 could be sent to each of the three schools)
Number of Percent Busing Cost per Student
Area Students 8th graders School A School B School C
1 100 50 $100 $0 $200
2 200 40 ----- $300 400
3 100 40 200 300 300
4 100 50 200 500 ----
5 200 60 0 ----- 200
School Capacity 200 300 500