Question $3\mathrm{.}4$

The Taxi Recapitalisation Project $($TRP$)$ was identified, introduced, and developed by the Minister of Transport to assess the effectiveness and efficiency of transforming the taxi industry. Thic TRP specifics eleven activities that cau be accomplished either by one person working alone or by several people working together. The activities, precedence constraints, and time estinates are shown in the following table:

$\backslash$table$[[$Activities$,$Preceding activities,Person$-$days required$],[$A$,-,15]]$

$\backslash$table$[[$B$,$A$,8],[$C$,$A$,5],[$D$,$B$,6],[$E$,$D$,8],[$F$,$C$,7],[$G$,$E$.$ F$,4],[$H$,$F$,2],[$I$,$F$,3]]\backslash$table$[[$J$,$H$,$ I,$3],[$K$,$J$.$G$,2]]$

NOTES:

You have five people who can be assigned on any given day.

A person must work full days on each activity.

The number of people working on an activity can vary from day to day.

REQUIRED:

$($i$)$ Prepare a network diagram $($use the AON format$)$ and calculate the critical path$($s$),$ the early start and finish times, the late start and finish times, as well as the total slack of each activity. Assume that only one person is working on each activity. Indicate how many person$-$days will be needed to complete this project.

$($ii$)$ Prepare a time chart $($Gantt chart$)$ for all the activities.

$($iii$)$ Use the time chart to prepare a daily personnel assignment sheet to complete the project within the shortest possible time. Also mention how many days the project could be compressed if unlimited personnel resources were available.

$($iv$)$ Will the company have to pay penalties if activities H and I are both delayed by nine days? How can the slack at activity J be used to overcome this problem?

$(3)$