Linear programming ( LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. The linear programming problem is to find a point on the polyhedron that is on the plane with the highest possible value. The surfaces giving a fixed value of the objective function are planes (not shown).
A closed feasible region of a problem with three variables is a convex polyhedron. The red line is a level set of the cost function, and the arrow indicates the direction in which we are optimizing. The optimum of the linear cost function is where the red line intersects the polygon. The set of feasible solutions is depicted in yellow and forms a polygon, a 2-dimensional polytope. A pictorial representation of a simple linear program with two variables and six inequalities. For the retronym referring to television broadcasting, see Broadcast programming.
