lisamuutujate

Lisamuutujad, also known as auxiliary variables or slack variables, are mathematical constructs used in optimization problems, particularly in linear programming. They are introduced to transform inequalities into equalities, thereby allowing the use of linear algebraic methods to solve the problem. In a standard form linear programming problem, inequalities are converted into equalities by adding non-negative slack variables. For example, the inequality constraint "x + y ≤ 10" can be rewritten as "x + y + s = 10" where "s" is a non-negative slack variable. This transformation does not change the feasible region of the problem but facilitates the application of the simplex method or other optimization algorithms. Slack variables play a crucial role in the formulation and solution of linear programming problems, enabling the conversion of inequality-constrained problems into equality-constrained ones. They are essential for the theoretical and practical aspects of linear programming, providing a systematic approach to handle constraints and optimize objective functions.