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 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 — 300 East 9 16 10 900 West 8 — 9 600 Central — 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. LO.1