Using a Lagrange multiplier is a method of finding an extreme value of a function with a constraint; for example, finding the extreme values of which is constrained by . This will occur when the contour lines of the function are parallel, the gradients will therefore be parallel as well (since the gradient vector is always orthogonal to the contour lines). As such, the Lagrange multiplier is a scalar such that Which results in four unknowns and four equations. This can be represented more concisely with the Lagrangian function