Consider a workshop with single machine. A customer has ordered the 10 different jobs expecting the delivery of any one job per week (means the due date for first job in processing sequence is 7, due dates for second job in processing sequence is 14, and so on). The processing time in days for each job is given in the table below. If a job is not delivered on expected time a penalty of 100 per job per day is imposed

Consider a workshop with single machine. A customer has ordered the 10 different jobs expecting the delivery of any one job per week (means the due date for first job in processing sequence is 7. due dates for second job in prpcessing sequence is 14, and so on). The processing time in days for each job is given in the table below. If a job is not delivered on expected time a penalty of 100 SR per job per day is imposed. Jobs Pi 1 7 2 5 3 8 4 3 5 9 6 6 7 9 8 4 9 5 10 4 a. Find the job processing sequence to minimize the penalty. b. Describe the environment, constraints and objective function clearly and give reason. c. Give the proof that, the sequence you find is optimal sequence (prove it using mathematical equation not by examples)