Throughout this problem set, let X = R?, and suppose a consumer faces a price vector p = (P1, P2) and has an income m, where p1, p2, m > 0. 1. [This question gives an example in which the consumer does not have an optimal solution.] Suppose (m, P1, P2) = (2, 1,2) and u takes the form u(x) = 1 +12 if