Expert: Steve Holleran - 2/21/2007

Question
thanks a lot for the response! tat helped a lot...some more queries...is problems involved with linear programming solved like how we solve simultaneous equations or is there any other technique by which we can solve those problems? pls do explain on the methods and techniques as to how to solve the linear programming problems.
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-----Question-----
could you pls tell me what linear programming is all about? where do we use them in real life? does it have something to do with simultaneous equations? and please do give me some links where i can get some notes/material for my reading/reference on linear programming.
-----Answer-----
Hello Harini,

Linear programming is a graphical method of solving problems involving a quantity to be maximized or minimized, in which there are a number of constraints placed on the variables involved in the problem.

Any high school Algebra 2 or Precalculus textbook, especially those published by McDougall/Littell or Prentice Hall, will have a section or two of linear programming problems.  The Prentice Hall book by Paul Foerster is especially good.

The method is basically graphing a system of lines which represent the constraints and shading certain regions of the graph to produce what is called a "feasible region" of solutions, and then testing the vertices of the region to determine the max or min value.  I've added a site with a good short description of this type of problem:

http://www.columbia.edu/~umk1/linprog.html

It is basically solving a system of simultaneous inequalities and then evaluating an objective function.

I hope you can find what you are looking for.

Steve Holleran

Answer
Hello again, Harini

I'm afraid my knowledge of linear programming doesn't extend too much further than what was in my previous reply.

There are a bunch of somewhat advanced techniques to solve more complicated problems than high-school level ones, but I am not very familiar with them.  One I know of is called the Simplex Method.  You can probably find out more about it by googling it, or getting hold of a college-level Linear Algebra text.  I think I may have worked with this  years ago--I'm talking the 1970's!--but I really don't remember much about it.

I'm sorry I can't be of more help here.

Steve Holleran