1.Consider the Interval Scheduling problem of Section 4.1. Consider the set of instances with n=4 requests, with the stipulation that each request must overlap with at least one other request. What is the maximum size of an optimal solution for any such instance?

2.Consider an instance of the Scheduling to Minimize Lateness problem with n=3 jobs. Let S be a schedule. What is the maximum number of inversions that S can have?

3.In the Scheduling to Minimize Lateness problem, an inversion in a schedule S was defined as a pair of jobs i and j such that i is scheduled before j but job j has an earlier deadline. Suppose the jobs are numbered 1, 2, ..., n in order of deadline. Let S be the schedule 6,1, 5, 4, 3, 2. How many inversions does the schedule S have?