Lineal programming (LP) is a powerful mathematical technique used for optimizing a linear función objetivo, which is subject to a set of linear inequalities or equations, known as constraints. The primary goal of linear programming is to find the best outcome, such as maximum profit or minimum cost, in a modelo matemático cuyas necesidades están representadas por relaciones lineales.
En un problema de programación lineal, la función objetivo es una ecuación lineal that represents the goal of the optimization, while the constraints are a set of linear inequalities that define the feasible region within which the solution must lie. The feasible region is typically a convex polygon in two dimensions, or a polytope in dimensiones superiores. Solutions to linear programming problems can be found using various algorithms, the most famous being the Simplex method, which efficiently navigates the vertices of the feasible region to find the solución óptima.
Linear programming is widely used in various fields, including economics, business, engineering, and military applications, where asignación de recursos and decision-making under constraints are critical. Examples include optimizing production schedules, minimizing transportation costs, and managing supply chains. The versatility and efficiency of linear programming make it an essential tool in operations research and analytics.