Consider the following maximization problem: Maximize: xy Subject to: x 2 + y 2 1 x 2 + 4y2 4 a. Find all the points and the corresponding lambda values that satises the Karush-Kuhn-Tuker conditions, if there are any. Show your work. b. Find all the points at which constraint qualication fails, if there are any. Show your work. c. Does the above maximization problem have a solution (explain). If it does nd all the solutions of the maximization problem. Show your work