What purpose slack variables and artificial variables are used in solving LPP?

Where, S1 is slack variable. Surplus & Artificial variables: They are used to convert Greater than or equal to (≥) constraint into equality to write standard form. Surplus variable is SUBTRACTED from ≥ constraint and Artificial variable is ADDED to the ≥ constraint.

Why do we use slack and surplus variables?

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. When a less-than-or-equal constraint is not binding, then there is some un-utilized, or slack, resource.

Why are surplus variables used in solving a linear programming problem by simplex method?

We call and surplus variables because they represent the amount that the left side of the inequality exceeds the right side. Surplus variables must be nonnegative. Now, to solve the linear programming problem, we form an initial simplex tableau as follows.

Why surplus and artificial variables are introduced?

In the equation which has the surplus variable, the artificial variable is introduced. In order to ensure that only the basic feasible solution needs to be considered, the nonnegative constraint is satisfied by the artificial variable. Consider the equation provided below which is involving the surplus variable .

What is the difference in between slack variable and surplus variable?

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.

Where are artificial variables used?

One type of variable introduced in a linear program model in order to find an initial basic feasible solution; an artificial variable is used for equality constraints and for greater-than or equal inequality constraints.

What is an artificial variable in linear programming?

The artificial variable refers to the kind of variable which is introduced in the linear program model to obtain the initial basic feasible solution. It is utilized for the equality constraints and for the greater than or equal inequality constraints. A variable also is known as a data item.