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/lagrange-multiplier-example-part-1 A Lagrange multipliers example of maximizing revenues subject to a budgetary constraint.