You work for a small business that plows driveways. Your city has experienced a major snowstorm so your boss, Mr. Plow, has lots of work to do! He has n clients who need some snow plowing done, and each job will take one hour to complete. All of the clients would prefer to have their driveways plowed earlier rather than later. More precisely, if client i is Mr. Plow's jth client, then client i's satisfaction is si = n j. Some clients are more important to Mr. Plow than others (perhaps they are paying more, are more likely to recommend Mr. Plow to others, or are more likely to be repeat customers in the future). Mr. Plow assign eachs client i a weight wi. You want to schedule Mr. Plow's clients across the n days such that you maximize the weighed sum of satisfaction, that is, P 1in wisi. The following greedy strategy finds an optimal ordering of clients: Complete the projects in decreasing order of wi. 1. [5 points] Use an exchange argument to show that this greedy strategy yields an optimal schedule