Problem 2. Scheduling with deadlines Given n jobs such that job j requires time t, and is due at time d;. We can schedule all jobs to minimize maximum lateness using the algorithm from the class. The proof of the optimality uses a key claim that exchanging two adjacent, inverted jobs does not increase the max lateness. Based on the proof, make 2 examples of this operation: one example, where the max lateness decreases after the swap and one example, where the max lateness does not decrease after the swap. Problem 2. Scheduling with deadlines Given n jobs such that job j requires time t, and is due at time d;. We can schedule all jobs to minimize maximum lateness using the algorithm from the class. The proof of the optimality uses a key claim that exchanging two adjacent, inverted jobs does not increase the max lateness. Based on the proof, make 2 examples of this operation: one example, where the max lateness decreases after the swap and one example, where the max lateness does not decrease after the swap