Consider the problem: Min 10 + a2 + y' subject to 2x2 +y 2 2, x 2 0 andy 2 0. I.y 1. Suppose that (r*, y") solves this problem. Is there necessarily a value of A* such that (r", y', A" ) satisfies the KTCs? Justify. 2 marks 2. Write down the KTCs and present the possible solutions. 3 marks 3. Are KTCs sufficient for the optimum to exist? Justify your answer. 1 mark 4. Find the optimal solutions for this problem. 1 mark