Problem 3. Consider a consumer with utility function u(x1, 2) = 1 + 12 + 12. (a) If pi = p2 = 1 and w = 4, solve the corresponding utility marimization problem and find x(pi. p2, w) ( which is x( 1, 1, 4) ) . (b) Can you find an example of pi, p2 and w such that the solution to the utility marimization problem x(p, p2, w) is a corner solution? (Hint: u($1, 12) +1 = (x] + 1)(2 + 1).)