2. (25) [Minimizing weighted sum of job completion times) Textbook Exercise 13 in Chapter 4. Consider a greedy strategy of scheduling a job with the largest ratio of customer weight over job processing time (i.e., W;/ti) first. Write a greedy algorithm based on this greedy strategy, and then prove or disprove that this greedy strategy is optimal. A high-level executable outline of algorithm is okay. In order to prove the optimality, use the exchange argument strategy (see the theorem 4.10 in the textbook page 131). In order to disprove it, present a counterexample that shows the greedy algorithm fails to minimize the weighted sum of the completion times. 2. (25) [Minimizing weighted sum of job completion times) Textbook Exercise 13 in Chapter 4. Consider a greedy strategy of scheduling a job with the largest ratio of customer weight over job processing time (i.e., W;/ti) first. Write a greedy algorithm based on this greedy strategy, and then prove or disprove that this greedy strategy is optimal. A high-level executable outline of algorithm is okay. In order to prove the optimality, use the exchange argument strategy (see the theorem 4.10 in the textbook page 131). In order to disprove it, present a counterexample that shows the greedy algorithm fails to minimize the weighted sum of the completion times