Question

Elaborate on the meaning of surplus and slack variables and also the standard form.

Answer 1

Surplus variable

A surplus variable refers to the amount by which the values of the solution exceeds the resources utilized. These variables are also known as negative slack variables . In the objective function, it carries a zero coefficient. In order to abtain the equality constraint , the surplus variable is added to the greater or equal to the type constraints. A variable refers to the number , characteristics, or quantity which can be counted or measured . A variable also is known as a data item. Some kinds of the variable are control variable , discrete variable, observed variable, dummy variable , binary variable and scale variable.

Slack variables

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.

The following is in standard form : A non negative variable that takes up the slack between the left hand side of an inequality and the right hand side is called a slack variable. The slack variable changes an inequality into an equation. And maximize 80x +70y becomes -80x -70y + M =0 for M as large as possible