Lagrange Multipliers

Lagrange multipliers are a mathematical method used to find the maximum or minimum of a function subject to certain constraints. Imagine you're trying to find the highest point on a hill while staying on a specific path; the method allows you to consider both the height of the hill (your function) and the path you must follow (your constraint). By introducing an additional variable (the Lagrange multiplier), you can adjust your calculations to take into account the constraint, helping you solve for the best possible outcome under those conditions. It's widely used in economics, engineering, and optimization problems.