I found it quite difficult to wrap my head around what was going on here, but the visuals that go along with Sal Khan's explanations on his website are very enlightening. He also does a good job of explaining the actual mathematics behind these type of optimization problems. I would definitely recommend watching the whole series in the link I am attaching below, as they were very beneficial to me. https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/lagrange-multipliers-and-constrained-optimization/v/constrained-optimization-introduction