$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$l$|\}$

$\backslash$hline ACTIVITY & $\backslash$begin$\{$tabular$\}\{$l$\}$

PREDECESSO $\backslash \backslash$

$\backslash (\backslash$mathbf$\{$R$\}\backslash )$

$\backslash$end$\{$tabular$\}$ & OPTIMISTIC & MOST LIKELY & PESSIMISTIC $\backslash \backslash$

$\backslash$hline A & $-$ & $3$ & $4$ & $5\backslash \backslash$

$\backslash$hline B & A & $2$ & $3$ & $4\backslash \backslash$

$\backslash$hline C & A & $4$ & $5$ & $6\backslash \backslash$

$\backslash$hline D & B & $4$ & $4$ & $4\backslash \backslash$

$\backslash$hline E & B & $2$ & $5$ & $6\backslash \backslash$

$\backslash$hline F & C$,$D$,$E & $2$ & $4$ & $5\backslash \backslash$

$\backslash$hline G & F & $2$ & $4$ & $6\backslash \backslash$

$\backslash$hline H & F & $4$ & $6$ & $7\backslash \backslash$

$\backslash$hline I & G$,$ H & $4$ & $6$ & $8\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

NB: Time periods are in months.

A$.$ Draw the activity network for this problem.

$[10$ marks$]$

B$.$ Determine the Expected Time and Variance for each activity.

$[10$ marks$]$

C$.$ Show the activity schedule $($EST$,$ EFT, LST$,$ LFT$)$ as well as slack. You may work in the network but please show the results in a table.

$[12$ marks$]$

D$.$ Determine and state the critical path for this project. $($This must be based on your work in c$)$ and not by inspection.

$[3$ marks$]$

E$.$ What are the expected time and the variance of the project?

$[2$ marks$]$

F$.$ What is the probability the project will be finished within $30$ months?

$[3$ marks$]$

$($Total $30$ marks$)$