2. (approx. 20 mins) (a) Solve the following optimization problem for a fixed a E (1, 11). V(a) = max{ax - x" +y}, subject to x ty 20, y20. (b) Totally differentiate the first order condition for x, and/or use your insights from (a) to find the sign of "7, i.e. how the optimal value of r changes with a > 0. (c) Use the envelope theorem to characterize the derivative of the value function V'(a) explicitly. Note: As a sanity check, the result you get in this part should be a 'formula in a', that is, no x*, y* should appear in its final formulation. (d) What is the solution to the optimization problem W(a) = max{(ax - x2 +y)3-5}, subject to x ty