Graphical Method

The graphical method is a tool used to solve LP problems which involve the use of two variables. It consists on the use of a cartesian coordinate system. In this system, each axis represents one variable. So, after having the cartesian plane represented, the restrains are drawn inside the plane as a straight line, and painting the feasible area (according to the sign of the inequality of each restriction). Later, when all of the restrictions are on the plane, if the problem has one optimal solution, it will be one of the vertices of the feasible area, which is the area that results from intercepting all the different curves, and all of the points within it, are solutions to the problem. If there is no feasible area, because there’s a contradiction between different restrictions, the problem has no solution. And there’s a third case, in which there are infinite solutions, and this happens when a restriction is parallel to the objective function.

The graphical method you will find in this tool asks you to fill in the coefficient of the objective function, select if you want to minimize or maximize, select if you want to consider negative values for the variables, add the restrictions and then, the program will solve the PL using the graphical method.