Question 2 (Interval Cover Redux, 30 points). Consider the interval cover from before, but with weights assigned to each interval. You are given a collection C of n intervals in the real line, each with an associated positive weight. Your goal is to find a set S of intervals from C so that no two elements of S overlap and so that subject to this, the sum of the weights of these intervals is as large as possible. Give an O(nlog(n)) time algorithm for this problem. Question 2 (Interval Cover Redux, 30 points). Consider the interval cover from before, but with weights assigned to each interval. You are given a collection C of n intervals in the real line, each with an associated positive weight. Your goal is to find a set S of intervals from C so that no two elements of S overlap and so that subject to this, the sum of the weights of these intervals is as large as possible. Give an O(nlog(n)) time algorithm for this