Use the method of Lagrange multipliers to determine the maximum and minimum values of the function f(x, y) = xy on the ellipse 4x2 + y- = 4. Question 8 [8] Consider the following NLP: maximise f(x, y) = 6x + 2xy - 2x2 - 2y2 subject to the constraint x + 2y - 2. 10 Show that the solution set x = and y = JIN 7 satisfies the following Kuhn-Tucker condi- tions: (8.1) The necessary condition. [4] (8.2) The sufficiency condition