Posted: September 13th, 2017

Brooks City

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 districtsnorth, 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 their districts, 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

District          Central School       West School    South School    Student 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 by using the computer.