# Linear Programming

4. Solve the following mixed integer linear programming model by using the computer

Maximize Z = 5X1 +6X2 + 4X3

Subject to

5X1 +3X2 + 6X3 ≤ 20

X1 + 3X2 + ≤12

X1, X3 ≥0

X2 ≥0 and integer

6. 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 Distance (miles) Student

Population Central West South 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 student 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

(See attached file)

I need some help solving these linear programming problems using ecel solver or QM for windows by computer. Please provide a detailed and easy to foowing solution. Thanks.

https://brainmass.com/math/linear-programming/linear-programming-288529

#### Solution Summary

A Complete, Neat and Step-by-step Solution for the two questions is provided in the attached Excel file.