Question

I completely understand the prof's explanation about the Lagrangian with one constraint - but I don't understand why the two constraint formulation works: i.e. L = f(x, y, z) + lambda1 g(x, y, z) + lambda2 h(x, y, z) = 0

Here f is the min/max function, and g and h are the two constraints. If there was no h, then the prof's explanation in lecture 39 makes completely sense in "matching up" the gradients of f and g with lambda1 as the scaler (where f = - lambda1 x g). But, I don't understand how the second constraint can simply be "added" to the Lagrangian equation. Thank you!