Consider the following problem in single machine scheduling with independent jobs.

job 1 2 3 4 5 6 7 8 Processing time (tj) 5 12 8 10 3 15 8 6 Due date (dj) 10 16 11 16 6 25 12 14 Weight (wj) 2 1 1 2 3 4 2 3 Obtain the optimal schedule for each of the following performance measures:

(a) To minimize mean flow time.

(b) To minimize the maximum lateness.

(c) To minimize weighted mean flow time.