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:

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 and solve the model using the computer.

b. The school board decided that because all students in the north and east districts must be bused, then at least 50% of the students who live in the south, west, and central districts must also be bused to another district. Reformulate the linear programming model to reflect this new set of constraints, and solve by using the computer.

c. The school board has further decided that the enrollment at all three high schools should be equal. Formulate this additional restriction in the linear programming model, and solve by using the computer.

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Distance (miles) Central West South Student District School School School Population North 8 11 14 700 South 12 9 - 300 East 9 16 10 900 West 8 - 9 600 Central 8 12 500