OPTIMIZATION TECHNIQUES IN REAL-WORLD PROBLEMS USING LAGRANGE MULTIPLIERS

Optimization plays a crucial role in applied mathematics, enabling the efficient use of resources under given constraints. One of the most powerful methods for solving constrained optimization problems is the Lagrange Multipliers technique. This paper explores the theoretical foundation of this method and demonstrates its application in real-world scenarios, including economics, engineering, and resource allocation. Through illustrative examples, the study highlights how the Lagrange method simplifies complex problems and provides optimal solutions under constraints.