# Operations Research and Optimization

Consider the linear programming problem

Minimize

x_1+x_2

Subject to

2 x_1 + x_2 leq 0

x_1 - 2x_2 geq 0

x_1/3 - x_2 =10

You are to transform this problem to a form suitable for feeding to programs expecting the standard forms below. In each part, record the matrices f, A, and b suitable for feeding to a software package expecting each of the standard forms.

Part I.

Find what the arrays f_I, A_I, and b_I need to be to solve this problem using a software package that requires the standard form

min fx, ,,, Ax leq b,

Part II.

Find what the arrays f_{II}, A_{II}, and b_{II} need to be to solve this problem using a software package that requires the standard form

min fx, ,,, Ax leq b, x geq 0

Part III.

Find what the arrays f_{III}, A_{III}, and b_{III} need to be to solve this problem using a software package that requires the standard form

max fx, ,,, Ax = b, x geq 0.

https://brainmass.com/math/optimization/operations-research-optimization-512954

#### Solution Summary

The solution discusses operations research and optimization.