Introductory Maths and Stats: Kuhn-Tucker Theorm...

Intuition: Since most economic constraints are inequality constraints not equality constraints, it makes sense for students to learn a bit about Kuhn-Tucker theory...to build intuition I like to draw pictures in order to demonstrate the different sets of complementary slackness conditions for a single variable function in both the maximization case and the minimization case.  There would be six diagrams that clearly emphasize the corner solutions v. the interior optimum, and the idea of a binding constraint versus a slack constraint.  Remember, if one of the constraints is slack the other MUST be binding!

Kuhn-Tucker Theorem: After building intuition with diagrams in the single variable case, I would jump straight to the Kuhn-Tucker theorem and the corresponding algorithm used to solve inequality constrained optimization problems.

General Case: The notes on the general case are confusing and I am not sure that they add to the student's understanding of how to apply Kuhn-Tucker.  I would recommend cutting the notes on the general case and spend more time working problems and making sure that the students understand the difference between slack constraints and binding constraints...