Slack and Surplus Variables-Standard form of LPP

Description:
Slack and surplus variables – standard form of LP models

Linear Programming – Standard Form/canonical form

Canonical form of standard LPP is a set of equations consisting of the ‘objective function’ and all the ‘equality constraints’ (standard form of LPP) expressed in canonical form.

What is meant by slack variable?
In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it into an equality. Introducing a slack variable replaces an inequality constraint with an equality constraint and a non-negativity constraint on the slack variable.

What is meant by surplus variable?
In an optimization problem, a surplus variable or negative slack variable is a variable that is subtracted to an inequality constraint to transform it into an equality. Introducing a surplus variable replaces an inequality constraint with an equality constraint and a non-negativity constraint on the surplus variable.

Slack and surplus variables in linear programming problem

A slack or surplus value is reported for each of the constraints. The term “slack” applies to less than or equal constraints, and the term “surplus” applies to greater than or equal constraints. If a constraint is binding, then the corresponding slack or surplus value will equal zero.

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