Design a greedy algorithm:

This problem appears in the textbook as exercise 4.13. You may want to also read the (longer) textbook description of this problem. Consider the following job scheduling problem. We are given n jobs and we have a single "machine" to process these jobs. Job i takes t time to complete. Suppose the machine starts at time t=0. Given a schedule (i.e., an ordering of the n jobs), let Ci denote the finishing time of job i. Each job has a weight wi that reflects its importance. The goal is to minimize the weighted sum of the completion times -, w;Ci. Design a greedy algorithm to solve this problem and prove its optimality using the "exchange argument" approach we discussed in class