36. 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 specified a Rs 5,000 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? (CA, May, 1994)

Activity Predecessors Optimistic Time Estimates (Weeks) Pessimistic Most likely A none B none 28 3 8 8 C A 7 11 9 D B 6 6 6 E C 9 11 10 F C 10 18 14 G C, D 11 11 11 H F,G 6 14 10 I E 4 6 5 J I 3 5 4 K H 1 1 1