Lagrange multiplier

Lagrange multipliers are a mathematical technique used to find the maximum or minimum of a function when there are constraints involved. Imagine you're trying to optimize a goal (like maximizing profit) while obeying certain rules (like a budget limit). Instead of solving both the goal and constraints separately, Lagrange multipliers combine them into one equation by introducing auxiliary variables (multipliers). This approach helps identify points where the function’s slope aligns with the constraints, revealing optimal solutions that satisfy all conditions efficiently.