Learn to identify the problems that can be solved with the help of linear programming. Examples of such problems include maximization of sales, fuel costs minimization, tax revenue maximization and consumer satisfaction maximization.
Learn how to solve a problem of linear programming by graphing the problem. You can only use this method when the mathematical model in question has only two variables. Then you can graph the solution on an X-Y graph. For example, if the equations are y<=3x, y>=x-2 and y=-(1/2)x+7, then you can plot a triangle on the X-Y graph that is made up of three lines: y=3x, y=x-2 and y=1(1/2)x+7. The triangle will represent a set of possible solutions. To find the best solution, graph the objective function as a vector and find the minimum or maximum points on the triangle.
Learn to solve linear programming problems with analytical methods. Analytical methods are fairly complicated and require a good understanding of algebra and calculus. The most popular analytical method is called the Simplex Method.
Learn to solve problems of linear programming with the help of computers--the way they are typically solved these days. The applications that you can use to solve linear programming problems include Mathcad, Excel Solver and ICO Xpress Optimization Suite.