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The Constraints with Slack Variables
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| Conclusions |
The simplex method needs functional constraints to be expressed
as equations. Therefore, slack variables are are used to convert functional
constraints with a 
sign into a functional constraint with an =
sign. The new form of these constraints becomes equivalent to the original
form by also adding nonegativity constraints for the slack variables. |
As shown on the right above, the new form of the functional
constraints provides a convenient system of equations for the simplex method.
It is also convenient for the simplex method to include the equation for
the objective function,
 ,
with this system of equations. After bringing the variables over to the
left-hand side, this additional equation becomes |
 |
| The last page will incorporate this into the overall problem. |