2. (35 PTS) Consider the function f(x, y) = x2+ y and the constraint x+ y = 1. Define the constrained optimisation problem max (x,y)ER s.t. xty=1 (i) (4 PTS) Check whether the conditions for Lagrange's theorem are satisfied. (ii) (6 PTS) Ignore the non-negativity constraints and solve the equality constrained optimisation problem. (iii) (4 PTS) Is this the global maximum? Explain your answer (iv) (10 PTS) Now incorporate the non-negativity constraints and solve for the optimum using the KKT conditions. (v) (6 PTS) Are the Lagrange functions you defined in (i) and (iv) concave? Can you say anything about the global maxima of the objective functions from your conclusion? (vi) (5 PTS) Interpret the results you obtained in (i) and (iv). If they were different, why