5. A construction company is preparing a PERT network for laying the foundation of a new art museum. Given the following set of activities, their predecessor requirements and three time estimates of completion time:

i. Draw the PERT network.
ii. Compute the slack for each activity and determine the critical path.
iii. The contract specifies a Rs. 5,000 per week penalty for each week the completion of the project extends beyond 37 weeks. What is the probability that this company will have to pay a maximum penalty of Rs. 15,000.

Activity Predecessors ABCD none none Optimistic 20 Time Estimates (Weeks) Pessimistic 4 Most Likely 8 8 A 7 11 389 B 6 6 6 E 9 11 10 F C 10 18 14 G C, D 11 11 11 H F. G 6 14 10 I E 4 6 J I K H 30 5 1 1 549