Mathematical modeling technique useful for guiding quantitative decisions in business, industrial engineering, and to a lesser extent the social and physical sciences. Solving a linear programming problem can be reduced to finding the optimum value (see optimization) of a linear equation (called an objective function), subject to a set of constraints expressed as inequalities. The number of inequalities and variables depends on the complexity of the problem, whose solution is found by solving the system of inequalities like a system of equations. The extensive use of linear programming during World War II to deal with transportation, scheduling and allocations of resources under constraints like cost and priority gave the subject an impetus that carried it into the postwar era. The number of equations and variables needed to model real-life situations accurately is large, and the solution process can be time-consuming even with computers. See also simplex method.
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