Graphical Method of Optimization: A Short Cut

Abstract

Although optimization problems are usually solved by computer, argument is presented that simpler cases can be handled by non-computer methods. A new, graphical method based on triangular systems of coordinates is presented. The triangular system described is usually considered an equilateral triangle. Each of the three sides of the triangle can be used as a coordinate axis for a variable in a suitable scale. Each combination of the three variables has a correspondent point in the triangle. The coordinates of a point inside the triangle represent the magnitude of each of the three variables, and can be read off of the corresponding scales. Two examples illustrate the application of this method. The method is compared with the Simplex method to show advantages and limitations.