O. Blažeková, P. Böhm, M. Vojteková

University of Žilina, The Faculty of Operation and Economics of Transport and Communications (SLOVAKIA)
Optimization problems are ubiquitous in the mathematical modeling of real world systems and cover a wide range of applications. These applications occur in all branches of economics, management, finance, telecommunication, materials science, engineering, computer science, and more. Many of these problems can be expressed as a linear programming (LP) task. LP deals with a class of optimization problems where both the objective function to be optimized and all the constraints are linear in terms of the decision variables. Linear programming is often a favorite topic for teachers and students. The possibility to present LP using a graphical approach, the relative simplicity of the solution method, widespread availability of LP software packages, and a wide range of applications make LP accessible even to students with relatively weak mathematical backgrounds.

The most widely used tool for solving the LP problem is an algebraic method - the Simplex Method proposed and developed by George Dantzing. However, the solution obtained by the algebraic method is sometimes not easy to interpret. If the number of decision variables is two, the LP problem can also be solved by more illustrative graphical method. The aim of our paper is to present the usage of the graphical method for solving LP tasks with three decision variables. This method provides a better understanding of the specific solutions related to an unbounded feasible region.