Question $2(10$ marks$)$:

The information of a project network is shown below.

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

$\backslash$hline Activity & $\backslash$begin$\{$tabular$\}\{$c$\}$

Precedence $\backslash \backslash$

Activities

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Optimistic $\backslash \backslash$

Time $\backslash \backslash$

$($rapks$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Most Probable $\backslash \backslash$

Time $\backslash \backslash$

$($wacks$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Pessimistic $\backslash \backslash$

Time $\backslash \backslash$

$($ragcks$)$

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

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

$\backslash$hline B & $-$ & $3$ & $3\mathrm{.}5$ & $7\backslash \backslash$

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

$\backslash$hline D & A$,$ C & $2$ & $3$ & $4\backslash \backslash$

$\backslash$hline E & B & $6$ & $10$ & $14\backslash \backslash$

$\backslash$hline F & B & $7\mathrm{.}5$ & $8\mathrm{.}5$ & $12\mathrm{.}5\backslash \backslash$

$\backslash$hline G & E & $4\mathrm{.}5$ & $6$ & $7\mathrm{.}5\backslash \backslash$

$\backslash$hline H & E & $5$ & $6$ & $13\backslash \backslash$

$\backslash$hline I & D$,$ G & $2$ & $2\mathrm{.}5$ & $6\backslash \backslash$

$\backslash$hline J & F$,$ H & $4$ & $5$ & $6\backslash \backslash$

$\backslash$hline

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

Determine the amount of slack associated with each activity using a forward and a backward pass method by completing the following table.

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

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$c$\}$

Activit $\backslash \backslash$

y

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Precedence $\backslash \backslash$

Activities

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Expected $\backslash \backslash$

Time $\backslash \backslash$

$($weeks$)$

$\backslash$end$\{$tabular$\}$ & $\backslash ($ E S $\backslash )$ & $\backslash ($ L S $\backslash )$ & $\backslash ($ E F $\backslash )$ & $\backslash ($ L F $\backslash )$ & Slack & Path? $\backslash \backslash$

$\backslash$hline A & $-$ & & & & & & & $\backslash \backslash$

$\backslash$hline B & $-$ & & & & & & & $\backslash \backslash$

$\backslash$hline C & B & & & & & & & $\backslash \backslash$

$\backslash$hline D & A$,$ C & & & & & & & $\backslash \backslash$

$\backslash$hline E & B & & & & & & & $\backslash \backslash$

$\backslash$hline F & B & & & & & & & $\backslash \backslash$

$\backslash$hline G & E & & & & & & & $\backslash \backslash$

$\backslash$hline H & E & & & & & & & $\backslash \backslash$

$\backslash$hline I & D$,$ G & & & & & & & $\backslash \backslash$

$\backslash$hline J & F$,$ H & & & & & & & $\backslash \backslash$

$\backslash$hline

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