Problem:
Brooks City Transportation Problem
Brooks City has three consolidated high schools, each with a capacity of 1,200 students. The school board has partitioned the city into five busing districts - north, south, east, west, and central - each with different high school student populations. the three schools are located in the central, west, and south districts. Some students must be bused outside of theri district, and the school board wants to minimize the total bus distance traveled by these students. The average distances from each district to the three schools and the total student population in each district are as follows.
Distance (miles)
Central West South Student
District School School School Population
North 8 11 14 700
South 12 9 0 300
East 9 16 10 900
West 8 0 9 600
Central 0 8 12 500
The school board wants to determine the number of students to bus from each district to each school to minimize the total busing miles traveled:
A. Formulate a linear programming model for this problem.
B. Solve the model using the computer. QM for Windows Preferred.