Mathematical methods in forming packages of economic problems

Abstract

Relevance of the study is determined by the growing need for systematic and reproducible formation of practical materials in economic disciplines under conditions of digitalization of the educational process and widespread use of automated tools for generating learning tasks. Traditional approaches to constructing economic problems based on random selection of numerical parameters do not ensure control over the properties of solution results and complicate their economic interpretation, which reduces the analytical value of practical tasks. The purpose of the article is to substantiate and develop an engineering approach to forming packages of economic problems based on mathematical models, which makes it possible to predefine key characteristics of solution results and ensure their correct and unambiguous economic interpretation. Research methods include analysis and generalization of approaches to the use of mathematical models in applied economic problems, structural and logical modeling of the process of forming practical materials, graphical analysis of results, and engineering design of schemes for controlled selection of mathematical model parameters. The results of the study establish the decisive role of a mathematical model as a tool for designing an economic problem, oriented not only toward the solution process but also toward shaping predefined properties of the result. It is proved that coordination of numerical and graphical results with the economic content of the model increases clarity and analytical value of practical tasks. Systemic limitations of traditional approaches associated with random parameter assignment and lack of control over result interpretability are revealed. The expediency of using controlled parameter selection and mathematical templates for automated generation of packages of homogeneous economic problems with stable economic interpretation is substantiated. Conclusions indicate that the application of an engineering scheme for forming economic problems based on mathematical templates makes it possible to increase reproducibility, clarity, and practical value of solution results, reduce the influence of random factors, and ensure systematic preparation of practical materials. Prospects for further research are associated with extending the proposed approach to more complex economic models, including nonlinear and multiparameter ones, as well as with evaluating the effectiveness of the engineering approach in various formats of digital learning environments.