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STAT 2112 Assignment 2 The city of Quatre Bras in Quebec has three consolidated high schools, each with a capacity of 1200 students

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STAT 2112 Assignment 2

The city of Quatre Bras in Quebec has three consolidated high schools, each with a capacity of 1200 students. The school board has partitioned the city into five busing districts ? north, south, east, west, and central ? each with different high school student population. The three schools are located in the central, west, and south districts. Some students must be bused outside of their district, and the school board wants to minimize the total bus distance travelled by these students. The average distances from each district to the three schools and the total student population in each district are as follows.

District Distance (miles) 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 in order to minimize the total busing miles travelled.

a. Formulate a linear programming model for this problem. Indicate the decision variables, objective function, and model constraints.

b. Solve the problem using the Excel Solver. Provide Excel Answer Report and Excel Sensitivity Report.