OPTIMAL ALLOCATION OF RESOURCES IN FURNITURE PRODUCTION: PROFIT MAXIMIZATION USING THE SIMPLEX METHOD

Аннотация

This in the article furniture working in the release optimal allocation of resources issueSimplex method using Furniture​ ​ ​ company's sixproduct type (chair ,table ,sofa, wardrobe , armchair , bed ) and six resource ( oil , cloth , metal , paint , labor ) power , energy ) based on structured linear programming model analysis The research is being conducted purpose – limited resources under the circumstances weekly profit maximize for the most good working release plan definition . Simplex of the method step calculations resulting in an optimal solution as 10 sofas and 10 wardrobes working release offer is 1100 thousand​ ​ soum​ maximum benefit brings . Article linear programming theoretical Basics , Simplex of the method practical application​ and his/her working release processes in optimization importance illuminates . Research results in real life economic problems solutionin doingmathematician models efficiency shows .​ Abstract:This article studies the issue of optimal resource allocation in furniture production using the Simplex method. A linear programming model of a furniture company based on six product types (chairs, tables, sofas, wardrobes, armchairs, beds) and six resources (wood, fabric, metal, paint, labor, energy) is analyzed. The purpose of the study is to determine the best production plan to maximize weekly profit under limited resources. As a result of step- by-step calculations of the Simplex method, the optimal solution is proposed to produce 10 sofas and 10 wardrobes, which will bring a maximum profit of 1,100 thousand soums. The article discusses the theoretical foundations of linear programming, the practical application of the Simplex method, and its importance in optimizing production processes. The results of the study demonstrate the effectiveness of mathematical models in solving real-life economic problems. Аннотация: В статье рассматривается задача оптимального распределения ресурсов при производстве мебели с использованием симплекс-метода. Проанализирована модель линейного программирования мебельной компании на основе шести типов продукции (стул, стол, диван, шкаф, кресло, кровать) и шести ресурсов (древесина, ткань, металл, краска, рабочая сила, энергия). Целью исследования является определение наилучшего плана производства для максимизации еженедельной прибыли в условиях ограниченных ресурсов. В результате пошаговых расчетов симплекс-метода оптимальным решением является изготовление 10 диванов и 10 шкафов, что принесет максимальную прибыль в размере 1 100 000 сумов. В статье page1240 INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE ISSN:2692-5206,ImpactFactor:12,23 AmericanAcademicpublishers,volume05,issue04,2025 Journal: https://www.academicpublishers.org/journals/index.php/ijai рассматриваются теоретические основы линейного программирования, практическое применение симплекс-метода и его значение в оптимизации производственных процессов. Результаты исследования демонстрируют эффективность математических моделей прирешенииреальных экономических задач. Kalit so‘zlar: mebel ishlab chiqarish, resurs taqsimlash, optimal yechim, simpleks usul, foydani maksimallashtirish, chiziqli dasturlash, ishlab chiqarish rejalashtirish, resurs cheklovlari, yog‘och, mato, metall, bo‘yoq, ishchi kuchi, energiya, divan, shkaf, matematik model,iqtisodiy samaradorlik,iteratsiya,pivotelement. Keywords: furniture production, resource allocation, optimal solution, simplex method, profit maximization, linear programming, production planning, resource constraints, wood, fabric, metal, paint, labor, energy, sofa, wardrobe, mathematical model, economic efficiency, iteration, pivotelement. Ключевые слова: производство мебели, распределение ресурсов, оптимальное решение, симплекс-метод, максимизация прибыли, линейное программирование, планирование производства, ограничения ресурсов, древесина, ткань, металл, краска, труд, энергия, диван, шкаф, математическая модель, экономическая эффективность, итерация,опорныйэлемент. Introduction . Processes research and optimal management – decision acceptance to doandsystems tooptimizescientific fields oriented .​ 1-Process research resources effective distribution for mathematician models , linear programming ,games​ theory andnetworks optimizationsuch as from methods uses . 2-Optimal management systems the most good management strategies determination with He is engaged in his work . main methods Pontryagin's Maximum principle and Bellman's dynamic programming . Literature analysis Furniture working in the release optimal allocation of resources and profit maximize issue modern economy and working to release management in the field important place​ This​ ​ topic according to literature mainly linear programming , Simplex method and resources effective management mathematician models around shaped . Linear programming main theory Developed by George Dantzig in 1947issued Simplex method with related​ is , this method resources distribution problems solution in doin