What is linear Programming?

    If you’re reading this page, more than likely you are a mathematics major considering taking a class in linear programming and game theory. Maybe you are fearful that linear programming requires many years of computer programming experience. In actuality, while computers may aid one in solving linear programming problems more efficiently, it is not for all practical purposes a “computer course”. It is a mathematics course, and in my opinion, one of the most interesting and rewarding. But to give credit where credit is due, knowledge of computers is a must if you plan on specializing in such a field. Because of the sheer size of some linear programming problems, they are almost humanly impossible to solve.

 Linear programming was developed largely by the mathematician George Dantzig, while attempting to solve problems associated with the US Air force, he developed a method referred to as “the simplex method.” This method is largely responsible for the success that linear programming has accomplished. A linear programming problem is one that entails the choice of an optimal set of values for certain variables that are subject to constraints. The objective of such a problem is to maximize or minimize your function. The function that you wish to maximize or minimize is referred to as your objective function. There are however certain criteria that define whether or not it is a linear programming problem. One can guess from the name, that in order for it to be a linear problem, it must be true that the constraints must be “linear”. This means that the variables can not be exponential (raised to a power). Some real world examples of linear programming problems aside from air force planning, include maximizing the revenue of your profits, optimum allotment of resources, and minimizing the cost associated with producing a product under many constraints; more generally, they may also be found in game theory and combinatorics. The possibilities are seemingly endless. It’s a great subject and an inspiring course for undergraduate as well as graduate mathematics.

 MIT offers an exceptional open courseware program that is available online. You can access a variety of mathematics courses free of charge at their web page. Available are a multitude of free on-line MIT classes which you can play on your computer. Go to http://ocw.mit.edu/OcwWeb/web/home/home/index.htm

 For more on linear programming (also from MIT) visit this link:

 http://ocw.mit.edu/NR/rdonlyres/Aeronautics-and-Astronautics/16-410Fall-2005/38AA4DDB-717B-4CBA-99DD-F273B691CCED/0/l8printrolinpgm.pdf.

-Rivkah Singh