Slack Variables : 

Slack variable represents an unused quaintly of  resources ; it is added to less than or equal (<) to type constraints in order to get an equality constraint.

Surplus  Variables :

A surplus variable represents the amount by which solution values exceed a resource. These variables are also called ‘Negative Slack Variables’ . Surplus variables like slack variables carry a zero coefficient in the objective function. it is added to greater than or equal to (>) type constraints in order to get an equality constraint.

Artificial Variables : 

  Artificial variables are added to those constraints with equality (=) and greater than or equal to ( > ) sign. An Artificial variable is added to the constraints to get an initial solution to an LP problem. Artificial variables have no meaning in a physical sense and are not only used as a tool for generating  an initial solution to an LP problem.

Particulars

Slack Variable

Surplus Variable

Artificial Variable

Mean

Unused resources of the idle resources.

Excess amount of resources utilized.

No physical or economic meaning. It is Fictitious.

When used ?

With <  Constraints

With >  Constraints

With > And = constraints

Coefficient

+1

-1

+1

Co-efficient in the Z – objective function

0

0

 -M for Maximization and +M for minimization

As Initial Program variable

Used as starting point.

Can’t be used since unit matrix condition is not satisfied

It is initially used but later on eliminated.

In Optimal Table

Used to help for interpreting idle & key resources.

–

It indicates the Infeasible Solution