Stats Assign 2 PDF

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4_20: 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: 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 and solve the model using the computer. Step 1: Decision variables District

Central School

North X1 South X4 East X7 West X10 Central X13 Step 2: Model constrains and summary

West School

South School

X2 X5 X8 X11 X14

X3 X6 X9 X12 X15

Student Population 700 300 900 600 500

Minimize Z= 8x1 + 11x2 + 14x3 + 12x4 + 9x5 + 0x6 + 9x7 + 16x8 + 10x9 + 8x10 + 0x11 + 9x12 + 0x13 + 8x14 + 12x15 X1 + x2 + x3 = 700 X4 + x5 + x6 = 300 X7 + x8 + x9 = 900 X10 + x11 + x12 = 600 X13 + x14 + x15 = 500 X1 + x4 + x7 + x10 + x13 = 250 X1 + x4 + x7 + x10 + x13 = 250 X1 + x4 + x7 + x10 + x13...