Slackvariabelen

Slackvariabelen is a term used in statistics and optimization to denote a variable introduced into an inequality constraint to convert it into an equality constraint. For example, an inequality of the form ax <= b can be rewritten as ax + s = b, where s is the slack variable. This slack variable s represents the "slack" or "room" between the left-hand side and the right-hand side of the original inequality.

In the context of linear programming, slack variables are crucial for transforming inequality constraints into a standard form that can be solved using algorithms like the simplex method. These variables are always non-negative, meaning s >= 0. If the original inequality was ax <= b, and s > 0, it implies that the constraint is not binding, meaning the left side is strictly less than the right side. If s = 0, the constraint is binding, and the left side is equal to the right side.

The introduction of slack variables allows for a more unified treatment of constraints within optimization problems. It simplifies the mathematical formulation and facilitates the application of various solution techniques. When solving a linear programming problem, the optimal solution will determine the values of the original variables as well as the slack variables. The values of the slack variables at the optimum provide important economic interpretations, often related to the marginal value of relaxing a constraint.