Solve the following problems: a. b. 1 1 min(x + y), subject to xzyz = 1 11 max(xzyz), subject to x + y = 2 Assume the consumer's maximization problem is as follows: max U = (x + 2) (y + 1) a. b. s. t. Pxx+Pyy B Set up the Lagrange function and solve for the optimal value. Check whether it is indeed the maximum. Minimize f(x, y) = 4ex+2 +2ey+5 subject to the constraint g(x, y) = x +y = 10 Set up the Lagrange function and solve for the optimal x and y value.