Question

123) Given (Time in weeks):

Activity	Optimistic	Most Likely	Pessimistic
A	3	4	5
B	6	7	14
C	2	3	10
D	6	9	12
E	4	5	12
F	1	3	11
G	1	2	9
H	2	5	8
I	1	4	7

Determine:

(a) the critical path. ( HOW DO I DO THIS WITH OUT A PREDECESSOR?)

(b) the probability that the project will be completed in 22 weeks.

Answer 1

Conver the table like this:

Activity	Optimistic time estimate(to)	4 * Most likely time estimate(tm)	Pessimistic time estimate(tp)	to+4tm+tp	Time estimate = to+4tm+tp/6
A	3	16	5	24	4
B	6	28	14	48	8
C	2	12	10	24	4
D	6	36	12	54	9
E	4	20	12	36	6
F	1	12	11	24	4
G	1	8	9	18	3
H	2	20	8	30	5
I	1	16	7	24	4

And without the predecessor, it's not able to calculate the critical path because, we never know how these paths are connected and we can randomly assume any paths to obtain our solution.

For example, If Source is A and destination is H, and

A,C,F,H might be a solution

AGDH might be a solution

and we get numerous amount of solutions and critical path can be calculated accordingly.

The probability can be calculated by No.of required cases/ total no.of cases. If you get 22 weeks for 3 paths out of 8, 3/8 will be your probability

Note: I tried my best answering the question. It'd be appreciated if you leave an upvote. Thanks in advance.