The following table represents a plan for a project code named Prometheus. The project plan consists of 11 activities code named P1 thru P11. The activity times - optimistic a, pessimistic b, and most likely m - and their precedence relationships in the table below.

	Predecessor Activities	Time In Days
Activities		a	m	b
P1	-	2	3	4
P2	P1	1	2	3
P3	P1	4	5	12
P4	P1	3	4	11
P5	P2	1	3	5
P6	P3	1	2	3
P7	P4	1	8	9
P8	P5, P6	2	4	6
P9	P8	2	4	12
P10	P7	3	4	5
P11	P9, P10	5	7	8

a) Construct the project network diagram. Make sure the diagram includes all the elements - early start, early finish, late start, late finish, and activity code name & time.

b) Indicate the critical path. What is the expected completion time of Prometheus? c) What is the probability that the project will take more than 30 days to complete?