MODELING ECONOMIC PROBLEMS BASED ON ELEMENTS OF LINEAR ALGEBRA

Abstract

This work provides a comprehensive examination of the role and importance of mathematical models in analyzing economic processes. Modern economic theory relies on mathematical methods that allow formal description of micro- and macroeconomic phenomena, identification of relationships between variables, and quantitative evaluation of these relationships. Mathematical modeling increases the accuracy of economic forecasts and supports efficient allocation of resources.

The use of matrices in economics, especially in solving optimal planning problems, plays a crucial role. The technological matrix describes the amount of resources required to produce each type of product. The production plan is represented in matrix–vector form, and the inequality AX ≤ B reflects the limitation of available resources. Determining the profit function and maximizing it over the set of feasible plans is the main goal of optimal planning.

The work provides detailed explanations of checking the feasibility of production plans, solving systems of linear equations, applying Cramer's rule, and transforming practical economic problems into mathematical models. Practical examples — such as transformer production and material cutting — demonstrate effective methods of solving economic problems mathematically. Overall, the study shows that mathematical modeling enables efficient decision-making, rational resource planning, and accurate economic forecasting.