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# Operations Research and Optimization

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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.