Question $2$:

$[20]$

You're managing a project to set up an automated sorting system for a parcel distribution centre. Each activity represents a major task in the project, and the times given are estimates of how long each task will take.

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

$\backslash$hline Activity & Description & $\backslash$begin$\{$tabular$\}\{$l$\}$

Time Estimate $\backslash \backslash$

$($days$)$

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

Immediate $\backslash \backslash$

Predecessors

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

$\backslash$hline A & Initial Planning & $5$ & $-\backslash \backslash$

$\backslash$hline B & Site Preparation & $4$ & $-\backslash \backslash$

$\backslash$hline C & Equipment Procurement & $6$ & A $\backslash \backslash$

$\backslash$hline D & Layout Design & $3$ & B $\backslash \backslash$

$\backslash$hline E & Power and Network Setup & $6$ & B $\backslash \backslash$

$\backslash$hline F & Installation of Software & $2$ & D $\backslash \backslash$

$\backslash$hline G & Equipment Assembly & $5$ & E $\backslash \backslash$

$\backslash$hline H & Testing & $8$ & C $\backslash \backslash$

$\backslash$hline I & Final Integration and System Testing & $5$ & F$,$ G $\backslash \backslash$

$\backslash$hline

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

$2\mathrm{.}1.$ Construct a network diagram for this process.

$2\mathrm{.}2.$ Determine ES$,$ EF$,$ LS$,$ LF and slack for each activity.

$2\mathrm{.}3.$ Determine the critical path and project completion time.

$(5)$