The table below gives durations of the remaining 10 tasks of an overdue project. There is only one machine to process these tasks. Until the project is completed, the factory needs to pay a penalty of $100 per day. A manager suggests to rent a second identical machine, at a fee of $80 per day, to reduce the project finishing time (makespan) and thus the penalty payment.

1. Determine the makespan and total penalty cost in the single machine case.

2. With a second machine, how would you schedule these tasks to minimize the project completion time? Present you schedule and determine the finish time of each machine.

3. Decide whether you want to rent the second machine by comparing the total cost with the single machine case.

4. In general, LST+LPT rule does not guarantee to minimize the makespan in all cases. But for this particular problem, the resulting makespan is the minimum one. Explain why.

C A | 8 B 3 4 D 6 E 15 F 10 G 12 H 7 I 9 J 4 C A | 8 B 3 4 D 6 E 15 F 10 G 12 H 7 I 9 J 4