Question 2: Suppose the objective function U (331 , 1:2) and its partial derivatives U5(:r;1, 3:2) belong to 01(E2). Moreover, U(:r:1,:c2) > 0 if and only if 2:1 > 0 and 3:2 > 0. For strictly positive parameters p = (331,132) and M, consider the following LagrangeProblem V(p, M) = HIEEEU($) subject to M p1:r:1 33232 = 0. 6 (a) Prove that, for given parameter p and M, the above LagrangeProblem always has a solution 35* = 33*(p, M) and, hence, V(p, M) is well dened. Assume that the matrix of the second partial derivatives _ 02U(1:*) 1f,- _ 13 333-3353 none of the other constraints is binding? Calculate this solution including the supporting multipliers explicitly. has the property that, for any real numbers (11 and 052, the equation 2 2 alum + (11:12am + (12111th + (3:211:22 = 0 holds if and only if (11 = 0:2 = 0. Moreover, assume without proof that the solution r*(p,M) is unique