What is the linear programming model?
A system of linear equations that can be used for control or modeling purposes.
"Linear" means that all of the equations used are in the form of lines. Non-linear equations may be "linearized" by various transformations, but in the end the entire set of equations must be in linear forms.
The linear form of equations allows them to be solved with interactions with each other. Thus, a change in one equation result may affect a series of other equations. That is what makes "modeling" possible. The "programming" is just another way to describe the mechanics of setting up the model in a linear form.
The beauty and utility of linear programming is that it can simulate very large inter-related processes, from traffic patterns to entire refineries. We regularly develop and use linear programming models to design and operate petroleum refineries and other chemical operations to optimize their economic return from a particular set of raw materials and market opportunities.
Linear programming is also at the heart of complex process control systems. It uses the inputs from sensors throughout a plant with a model (the program) of the plant performance to adjust control outputs to devices in the plant. Those maintain the safe and economic operation of the plant.