Abstract: Mathematical optimization techniques are essential tools for effective resource management across various fields, including agriculture, manufacturing, energy, transportation, and environmental management. This research paper explores the application of different mathematical optimization methods, such as linear programming, integer programming, dynamic programming, and heuristic approaches, in addressing resource allocation and management challenges. Through detailed case studies, we demonstrate how these techniques enhance decision-making, improve efficiency, and contribute to sustainability. The findings highlight the significance of optimization models in optimizing resource utilization and fostering sustainable practices.