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 which minimizes
the quantity subject to the constraints and for .
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