Linear Programming

Linear programming is a very useful function of mathematics that allows one to place all the constraints and feasible profits on a graph. This is done with the use of inequalities. Each constraint, for example, “The amount of people that can be trained at one base can not exceed 600” can be created into an inequality, such as P≤600. This can be plotted on a graph as an inequality, with several others. Eventually, there will be an area that is shaded, and there are no points outside of it which can possibly be achieved. This is called the feasible set, and it includes all the options possible for the financial problem. To achieve the most profitable point, one must know the value for the unit on each axis. Since the best possible profit is as close to the outside as one can get, this point lies at the intersection of two or more of these inequalities. By changing the values of the units, the most profitable combination can also be changed, since the slope of the values changes.

For linear programming, it is not always necessary to use a graph. In fact, in many cases it is much easier not to. Once you have eliminated all the points of intersection which are not in the feasible set, and are left with the ones that are, all that is left to do is to try each of these intersection points with the values of the units, and compare them against each other. The point with the most desirable profit is the solution to your problem. This is very beneficial for problems with more than two units. This is because it is nearly impossible to look at a three-dimensional inequality graph, and impossible to graph anything with more than three dimensions.