This course explores the mathematical theory and computational methods for finding the optimal solution to complex problems under specific constraints. The curriculum focuses on linear, non-linear, and integer programming, as well as the Simplex method and duality theory. Students learn to formulate real-world challenges into mathematical models and solve them using optimization software and algorithms. The course emphasizes sensitivity analysis and the application of dynamic programming to resource allocation. By the end of the semester, students will be capable of optimizing industrial processes, logistics, and financial systems through rigorous mathematical modeling and algorithmic execution.