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Apr
30

Linear Programming — from Wolfram MathWorld








Linear programming, sometimes known as linear optimization, is the problem of maximizing or minimizing a linear function over a convex polyhedron specified by linear and non-negativity constraints. Simplistically, linear programming is the optimization of an outcome based on some set of constraints using a linear mathematical model.

Linear programming is implemented in the Wolfram Language as LinearProgramming[c,
m, b], which finds a vector x which minimizes
the quantity cx subject to the constraints mx>=b and x_i>=0 for x=(x_1,...,x_n).

Linear programming theory falls within convex optimization theory and is also considered to be an important part of operations
research
. Linear programming is extensively used in business and economics, but
may also be used to solve certain engineering problems.

Examples from economics include Leontief’s input-output model, the determination of shadow prices, etc., an example of a business application would be maximizing profit in a factory that manufactures a number of

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