ECONOMIC PROBLEMS IN LINEAR AND NONLINEAR PROGRAMMING: THE GRAPHICAL METHOD AND THE METHOD OF LAGRANGE MULTIPLIERS

Abstract

This scientific work examines key economic optimization problems that arise in both linear and nonlinear programming contexts. The graphical method is presented as an intuitive tool for solving two-variable linear programming problems, including resource allocation and production planning. The method of Lagrange multipliers is explored as a powerful technique for nonlinear constrained optimization, with applications to cost minimization and utility maximization in economics. Illustrative numerical examples demonstrate both methods in practical economic settings.