Pik-Fast, a chain of convenience stores, is planning to open a new store. The activities required, their immediate predecessors, and the optimistic, most likely, and pessimistic estimates of their times (in days) are provided below.

Activity	Description	Immediate Predecessors	Optimistic Time (days)	Most Likely Time (days)	Pessimistic Time (days)
A	Select manager	--	10	12	20
B	Select site	--	8	15	22
C	Hire workers	A	17	21	31
D	Basic training	C	3	4	5
E	Secure permits	B	12	18	30
F	Construct building	E	26	30	40
G	Purchase equipment	--	30	45	60
H	Install equipment	F,G	4	6	8
I	Advertise opening	B	15	55	89
J	Final training	D,H	2	3	4
K	Stock store	H,I	4	6	8
L	Open store	J,K	1	1	1

a) Provide the project network.

b) Identify the critical path and projected project completion time using the expected completion times.

c) Calculate the expected slack times for any path not including the critical path. For the path slack time, compute this compared to the critical path and that also considers the slack time for each activity on that path.

d) Find the probability that the critical path will be completed within 80 working days.

e) Illustrate or explain why the probability that the critical path will be finished in 80 days or less is not necessarily the probability that the project will be finished in 80 days or less. Assume that times for each activity will not change from what is provided above and no new activities are added nor are the predecessor relationships changed.