b) Activity schedule.

Activity y	Optimistic (o)	Most probable(M)	Pessmistic (p	Expected Time (o+4M+P)/6	Variance [(P-o)/6]2
A	1.5	2	2.5	2	0.03
B	2	2.5	6	3	0.44
C	1	2	3	2	0.11
D	1.5	2	2.5	2	0.03
E	0.5	1	1.5	1	0.03
F	1	2	3	2	0.11
G	3	3.5	7	4	0.44
H	3	4	5	4	0.11
I	1.5	2	2.5	2	0.33

.

c) Critical Activities

Activity	Earliest Start	Latest Start	Earliest Start	Latest Start	Slack	Critical ACTIVITY
A	0	0	2	2	0	Yes
B	2	2	5	5	0	Yes
C	0	1	2	3	1
D	2	3	4	5	1
E	5	10	6	11	5
F	6	11	8	13	5
G	5	5	9	9	0	Yes
H	9	9	13	13	0	Yes
I	13	13	15	15	0	Yes

Therefore the critical path will be ABGHI.

Expected Completion time=2+3+4+4+2=15

d) Variance of the critical path will be the sum of variances of all the critical activities:

2=0.03+0.44+0.44+0.11+0.03=1.05

At 0.99probability

z=+2.33

Z=TE(T)

Z=[T15)(1.05)12

Z=2.23

Now,

T=15+2.23(1.05)12

T=17.4 weeks

e) If the training program would be ready earlier, it could be advertised earlier and there would be more paying attendees. Therefore, it is worth to invest in crashing preparation times. By using the values of max. reduction times in days and crash costs in $ per day and the fact that a week has 5 working days, formulate and write down a linear programme model that minimizes the cost to crash the total project time by one week. \begin{tabular}{|c|l|c|c|c|c|c|c|} \hline & & Immed. & \multicolumn{2}{|c|}{ Time (in weeks) } & Max. Red. & Crash \\ Act. & Description & Predec. & OptiMost mist. & PessiProb. mist. & Time (in days) & Cost/d (in \$) \\ \hline A & Plan topic & & 1.5 & 2.0 & 2.5 & 2 & 30 \\ B & Obtain speakers & A & 2.0 & 2.5 & 6.0 & 3 & 10 \\ C & List meeting locations & & 1.0 & 2.0 & 3.0 & 2 & 30 \\ D & Select location & C & 1.5 & 2.0 & 2.5 & 2 & 30 \\ E & Finalize speaker travels & B,D & 0.5 & 1.0 & 1.5 & 1 & 20 \\ F & Final check with speakers & E & 1.0 & 2.0 & 3.0 & 2 & 30 \\ G & Prepare and mail prochure & B,D & 3.0 & 3.5 & 7.0 & 3 & 20 \\ H & Make Hotel reservations & G & 3.0 & 4.0 & 5.0 & 4 & 10 \\ I & Handle last-minute updates & F,H & 1.5 & 2.0 & 2.5 & 1 & 20 \\ \hline \end{tabular}