The article explores the implementation of digital and mathematical technologies in decision support systems (DSS) aimed at enhancing the efficiency of livestock enterprises. In the context of digital transformation and increasing uncertainty in agriculture, the authors emphasize the importance of intelligent DSS capable of processing large datasets and supporting rapid, evidence-based decision-making. The purpose of the study is to identify effective technological and methodological approaches for optimizing livestock management, particularly in the area of animal feeding. Methods include the use of mathematical models, predictive algorithms, automated control systems, and big data analytics. The proposed DSS architecture enables real-time monitoring, adaptive ration formulation, and integration of physiological, environmental, and economic data. The paper provides practical examples of successful DSS applications, such as automated milking systems and health monitoring technologies, and analyzes their impact on productivity and cost reduction. A set of methodological recommendations is formulated to enhance management efficiency, including modular system design, staff training, and integration of IoT and AI technologies. The article concludes that intelligent DSS not only reduce feeding costs but also improve animal health, optimize resource use, and support sustainable agricultural practices. The results are of practical significance for researchers, developers, and farm managers aiming to implement data-driven solutions in livestock production.

Keywords: diversification of management, production diversification, financial and economic purposes of a diversification, technological purposes of ensuring flexibility of production

The purpose and objectives of this work is to develop methods of iterative methods for solving systems of linear equations. Achieving the goals and objectives achieved by the development of an iterative method using the apparatus q-differentiation. With the software package Matlab Computational experiments, which resulted in the performance of the proposed method is confirmed.

Keywords: system of linear equations, the objective function, the gradient method, iterative method, modeling, algorithm, function extremum, q-derivative, relative error, norm of the vector, the conditionality of the problem