Enter the characters you see below Sorry, we just need to make sure you’re not a robot. Jump to navigation Jump to search “Linear problem” redirects here. It is not to be confused with Linear function. About programming paradigms pictorial representation of a simple linear program with two variables and six inequalities.

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The set of feasible solutions is depicted in yellow and forms a polygon, a 2-dimensional polytope. A closed feasible region of a problem with three variables is a convex polyhedron. The linear programming problem is to find a point on the polyhedron that is on the plane with the highest possible value. Linear programming can be applied to various fields of study.

It is widely used in mathematics, and to a lesser extent in business, economics, and for some engineering problems. Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. In 1939 a linear programming formulation of a problem that is equivalent to the general linear programming problem was given by the Soviet economist Leonid Kantorovich, who also proposed a method for solving it. Dantzig independently developed general linear programming formulation to use for planning problems in US Air Force. Dantzig’s original example was to find the best assignment of 70 people to 70 jobs.