Weighted shortest processing time first rule we want to

Question

(Weighted Shortest Processing Time First Rule) We want to schedule N tasks, the ith of which requires Ti time units. Let ti denote the time of completion of the ith task, i.e.,

Let wi denote a positive weight indicating the importance of early completion of the ith task. Use an interchangeto show that in order to minimize the total weighted completion time we must order the tasks in decreasing order of w_i/T_i.