PERT$-$ Extra Practice $1$

P$1)$ For the following proposed engineering project,

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

$\backslash$hline Activities$/$Tasks & $\backslash$begin$\{$tabular$\}\{$c$\}$

$\backslash (\backslash$mathrm$\{$t$\}\_\{\backslash$mathrm$\{$o$\}\}\backslash )\backslash \backslash$

$($days$)$

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

$\backslash (\backslash$mathrm$\{$t$\}\_\{\backslash$mathrm$\{$m$\}\}\backslash )\backslash \backslash$

$($days$)$

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

$\backslash (\backslash$mathrm$\{$t$\}\_\{\backslash$mathrm$\{$p$\}\}\backslash )\backslash \backslash$

$($days$)$

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

Precedence $\backslash \backslash$

Relationship

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

$\backslash$hline A & $2$ & $4$ & $6$ & $\backslash \backslash$

$\backslash$hline B & $4$ & $6$ & $9$ & A $\backslash \backslash$

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

$\backslash$hline D & $5$ & $8$ & $10$ & A $\backslash \backslash$

$\backslash$hline E & $4$ & $6$ & $8$ & D $\backslash \backslash$

$\backslash$hline F & $3$ & $5$ & $7$ & B$,$ C $\backslash \backslash$

$\backslash$hline G & $3$ & $4$ & $6$ & B $\backslash \backslash$

$\backslash$hline H & $2$ & $5$ & $7$ & E$,$ F $\backslash \backslash$

$\backslash$hline I & $4$ & $7$ & $11$ & E$,$F $\backslash \backslash$

$\backslash$hline J & $3$ & $6$ & $8$ & H$,$ I, G $\backslash \backslash$

$\backslash$hline K & $1$ & $4$ & $8$ & J $\backslash \backslash$

$\backslash$hline

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

a$)$ Draw the logic network diagram and determine what will be the critical path and project duration using PERT analysis.

b$)$ What is the floating time for activity F and H $?$

c$)$ Based on the PERT analysis, if you wanted to be $\backslash (90\backslash \%\backslash )$ certain that the project will be completed on time, what project duration would you promise in your proposal?