Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/lagrange-multipliers-and-constrained-optimization/v/meaning-of-lagrange-multiplier In the previous videos on Lagrange multipliers, the Lagrange multiplier itself has just been some proportionality constant that we didn't care about. Here, you can see what its real meaning is.