Show all work please.

Al and Bill are arguing about the performance of their sorting algorithms. Al claims that his O(N log N)-time algorithm is always faster than Bill's O(N2)-time algo- rithm. To settle the issue, they implement and run the two algorithms on many randomly generated data sets. To Al's dismay, they find that if N 1000 the O(N2)- time algorithm actually runs faster, and only when N 1000 the 0(N logN)-time (10 pts.) one is better. Explain why the above scenario is possible. You may give numerical