Mathematical optimization applied to an agricultural unit in Western Paraiba/Otimizacao matematica aplicada a uma unidade agropecuaria no Oeste Paraibano/Optimizacion matematica aplicada a una unidad agropecuaria en el Oeste Paraibano

The present study aimed to develop a mathematical model for a small agricultural production unit in the western Paraibano, with the goal of maximizing economic outcomes. The rapid technological and scientific advancements of recent decades have enabled the development of specialized software for modeling and solving optimization problems. These software tools have become essential for supporting decision-making in operational management. The work was conducted on a rural property located in the interior of the municipality of Alagoa Nova, Paraiba. To achieve this, it was necessary to understand the dynamics of the agricultural production system of the property by using interviews, questionnaires, and cost estimates. This procedure allowed for the collection of data that aided in the investigation and analysis of the production unit, resulting in the formulation of a mathematical model and the development of alternative development strategies adapted to the reality of the rural property. Based on the collected data, economic calculations were performed using LINGO software, taking into account the intake of forage by the cattle of the unit. Technical, financial, surface, and labor constraints were established. It was found that mathematical modeling is an effective tool, as it provides an analysis of complex problems, allows for scenario simulation, and evaluates the potential consequences of decisions, reducing risks, optimizing the use of natural resources and inputs, minimizing waste, and maximizing productivity. This approach improves economic efficiency and promotes more responsible agricultural practices. This study contributes to the understanding and enhancement of optimization techniques in agricultural management. Keywords: Mathematical Modeling. Production System. Beef Cattle. Animal and Plant Protein. O presente estudo teve como objetivo, desenvolver um modelo matematico para uma pequena unidade de producao agropecuaria no oeste paraibano visando maximizar o resultado economico. O rapido avanco tecnologico e cientifico das ultimas decadas possibilitou o desenvolvimento de softwares especializados em modelar e resolver problemas de otimizacao. Esses softwares podem tornaram-se ferramentas essenciais para apoiar a tomada de decisoes na gestao de operacoes. O trabalho foi desenvolvido em uma propriedade rural, localizada no interior do municipio de Alagoa Nova, Paraiba. Para isso, foi necessario compreender a dinamica do sistema de producao agropec