3. Spectrum Problem: You want to create a scientific laboratory capable of monitoring any frequency in the electromagnetic spectrum between L and H. You have a list of possible monitoring technologies, Ti, i = 1, ..n, each with an interval [li , hi] of frequencies that it can be used to monitor. You want to pick as few as possible technologies that together cover the interval [L, H]. Candidate Greedy Strategy I: First, buy the technology that covers the longest sub-interval within (L, H). (i.e.,The longest interval (l, h), but not including the sub-intervals (l, L) and (H, h) outside the interval we need covering.) At each subsequent step, buy the technology that covers the largest total length that is still uncovered. Candidate Greedy Strategy II: Look at all the technologies with l L. Of these, buy the one Ti = (li , hi) with the largest value of hi . Repeat the process to cover the remaining interval, (hi, H). Your Job: Discuss which approach (1 or 2 or both) is the optimal solution. You need to come up with examples to support your claim. For example, choose a numberline and intervals with numbers and examine what happens to conclude your desicion.