What is a slack variable?
Understand the Problem
The question is asking about the concept of a slack variable, which is often used in optimization problems, particularly in linear programming. A slack variable represents the difference between the left side and the right side of a constraint when the left side is less than the right side, allowing for a constraint to be met without making it an equality.
Answer
A non-negative variable added to an inequality constraint to convert it into an equality constraint.
A slack variable is a non-negative variable added to an inequality constraint in an optimization problem to transform it into an equality constraint.
Answer for screen readers
A slack variable is a non-negative variable added to an inequality constraint in an optimization problem to transform it into an equality constraint.
More Information
Slack variables are particularly important in the simplex method for solving linear programming problems. They essentially 'absorb' any excess quantity in resource constraints, ensuring that equality is achieved without violating the original inequality restrictions.
Tips
Common mistakes include forgetting that slack variables must be non-negative and misinterpreting their role in transforming inequalities into equalities.
Sources
- Slack variable - Wikipedia - en.wikipedia.org
- Slack Variable Tutorial | Design Optimization - APMonitor - apmonitor.com
- Define the concept of slack variables in linear programming. - tutorchase.com
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