Problem 1 (20 points) Suppose you are given two sets A and B, each containing n positive integers. You can choose to reorder each set however you like. After reordering, let ai be the i-th element of set A, and let bi be the i-th element of set B. You then receive a payoff on 11=1 aGive an algorithm that will maximize your payoff (6 points). Prove that your algorithm maximizes the payoff (10 points) and state its running time (4 points)