You are running a software company and have a series of n jobs that must be pre-processed first on a supercomputer before being moved to a smaller PC. You have only one super- computer, but you have n PCs so the second stage can be performed in in parallel. More specifically, your jobs are described as J- (s1f), J2 (22).., Jn-(Sn,n), where job J needs si units of time to be pre-processed on the super-computer and fi units of time on the PC You need to work out an order in which to give the jobs to the super-computer. As soon as the first job is done on the super-computer, it can be moved to the PC for finishing; at that point a second job can be given to the super-computer; when the second job is done it can go straight to a PC since the PCs can work in parallel, and so on. So if the jobs are processed in the order given, job J finishes at time (sk) fi. A schedule is an ordering of the jobs to be given to the super-computer. The completion time is the point at which all jobs have finished being processed on the PCs. We wish to minimize the completion time. (a) Give an efficient (greedy!) algorithm for computing the optimal order in which to proces the jobs so that the completion time is minimized. (b) Describe the greedy choice your algorithm makes and show that it is correct.