Lineaariohjelmointia

Lineaariohjelmointia, or linear programming in English, is a mathematical method for optimizing a linear objective function subject to linear equality and inequality constraints. The goal is to find the best possible outcome, such as maximum profit or minimum cost, in a mathematical model.

The core components of a linear programming problem include an objective function, which is a linear expression that needs to be maximized or minimized, and a set of constraints, which are linear inequalities or equalities that define the feasible region. The feasible region represents all possible combinations of decision variables that satisfy the constraints.

Linear programming techniques are widely used in various fields, including operations research, economics, and engineering. Applications include resource allocation, production planning, scheduling, and transportation logistics. For example, a company might use linear programming to determine the optimal mix of products to manufacture to maximize profit, given limited resources like labor and raw materials.

The solution to a linear programming problem can be found using various algorithms, with the simplex method being one of the most well-known. If the feasible region is non-empty and the objective function is bounded, a solution exists. If the feasible region is empty, there is no solution. If the objective function is unbounded, the optimal solution may not exist.