We are to complete a set of n jobs using m identical machines. Each job has a known duration. The goal is to schedule the jobs on m machines so that the time to finish the last job is as small as possible. Once a job is scheduled on a machine, it can’t be stopped and restarted. Any job can run on any machine. A greedy algorithm to solve this problem is as follows: sort jobs in decreasing order of duration. Schedule jobs one by one, choosing the machine where it can start the earliest. a. For m = 3 and n = 6 where the durations are <9, 12, 3, 8, 6, 5>, what is the finish time of the last job using greedy schedule? b. Exhibit an input for which the greedy schedule is NOT optimal

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