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Slack variable

Slack variable

Overview
In Linear programming
Linear programming
In mathematics, linear programming is a technique for optimization of a linear objective function, subject to linear equality and linear inequality constraints...

 a slack variable is a variable that is added to a constraint to turn the inequality into an equation.
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Encyclopedia
In Linear programming
Linear programming
In mathematics, linear programming is a technique for optimization of a linear objective function, subject to linear equality and linear inequality constraints...

 a slack variable is a variable that is added to a constraint to turn the inequality into an equation.
This is required to turn an inequality into an equality where a linear combination of variables is less than or equal to a given constant in the former. As with the other variables in the augmented constraints, the slack variable cannot take on negative values, as the Simplex algorithm
Simplex algorithm
In mathematical optimization theory, the simplex algorithm, created by the American mathematician George Dantzig in 1947, is a popular algorithm for numerically solving linear programming problems...

requires them to be positive or zero.

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