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Linear Programs in Standard Form

Before we start discussing the simplex method, we point out that every linear program can be converted into ``standard'' form

eqnarray34

where the objective is maximized, the constraints are equalities and the variables are all nonnegative.

This is done as follows:

example60

Let us first turn the objective into a max and the constraints into equalities.

tex2html_wrap_inline538

The last step is to convert the unrestricted variable tex2html_wrap_inline540 into two nonnegative variables: tex2html_wrap_inline542 .

tex2html_wrap_inline544


Michael A. Trick
Mon Aug 24 14:57:03 EDT 1998