The applications are in finding optimum solutions to a linear objective function, subject to a number of linear constraints.
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Linear programming is basically used to maximize profits (or some other function), when you have certain restrictions (for example, a limited amount of several resources).
Linear programming approach does not apply the same way in different applications. In some advanced applications, the equations used for linear programming are quite complex.
Accurate linear measurement.
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For compressor applications with critical valve outflow it is linear, and possibly equal percentage. Applications with sub-critical outflow need more analysis.
Linear transformations can be very important in graphics. Also, linear transformations come up whenever you need to solve systems of linear equations, which arise quite often. Finally, they can be useful in further areas of mathematics such as topology.