# Slack, Surplus, and Artificial Variables

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1. What are slack, surplus, and artificial variables? When is each used and why?

2. Discuss the similarities and differences between minimization and maximization problems using the graphical solution approaches of linear programming.

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##### Solution Summary

This solution explains the conceps of surplus, slack and artificial variables. Additionally, this solution compares and contrasts minimization and maximization problems using the graphical solution approaches of linear programming.

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Slack, Surplus and Artificial Variables

A slack variable is a variable that is added to inequality equation constraints with less than or equal to signs changing them into equalities. Introducing a slack variable to an inequality constraint transforms the inequality into a non-negativity equality constraint and is, in most cases, required to be a positive value. This variable is often used when working out inequalities using simplex method to determine optimum values, and is often applied less than or equal to inequalities (Arsham, 1997).

A surplus variable on the other hand is a variable that transforms a greater than or equal to inequality constraint in to equality constraints and is often in most cases a negative value. Introducing a surplus variable to an inequality constraint often transforms it into ...

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