Surplus variable

In Linear programming a surplus variable is a variable which is subtracted from 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 greater than or equal to a given constant in the former. As with the other variables in the augmented constraints, the surplus variable cannot take on negative values, as the Simplex algorithm requires them to be positive or zero.

Example

By introducing the surplus variable $\mathbf {y} \geq 0$, the inequality $\mathbf {A} \mathbf {x} \geq \mathbf {b}$ can be converted to the equation $\mathbf {A} \mathbf {x} -\mathbf {y} =\mathbf {b}$.

   if the constraint of l.p.p is 4x1+5x2≥25

then the non negative variable s2 which satisfies 4x1+5x2-s2=25 is called a surplus variable.

the variable s2 is called surplus variable because surplus=production-requirement

See also

• Slack variable
• Simplex algorithm