A project consists of nine activities whose time estimates (in weeks) and other characteristics are given below:

(i) Show the PERT network for the project.
(ii) Identify the critical activities.

(iii) What is the expected project completion time and its variance?

(iv) What is the probability of completing the project one week before the expected time?
(v) If the project is required to be completed by December 31 of a given year and the manager wants to be 95% sure of meeting the deadline, when should he start the project work?
(vi) A penalty of Rs 15,000 per week is to be imposed on the contractor if the project is not completed in 36 weeks. What is the probability that he has to pay a penalty? a penalty of Rs 45,000?

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Activity Preceding activity(ies) Most optimistic 2 Time estimates (weeks) Most likely Most pessimistic ABCDEFGH 4 6 CO 6 co 6 6 6 12 24 A 2 5 A 11 B, D 8 B, D 3 C, F 9 E 4 10650 14 23 12 27 8 26 9 16