Question $3$: Project Scheduling

$[22$ marks$]$

Consider the following project schedule

$\backslash$table$[[$Activity ID$,$Predecessor,Duration $($weeks$)],[$A$,$NONE,$3],[$B$,$NONE,$7],[$C$,$NONE,$6],[$D$,$C$,5],[$E$,$B$,9],[$F$,$B$,5],[$G$,$F$,7],[$H$,$A$,4],[$I$,$D$,$E$,$G$,8]]$

$($a$)$ Draw a Gantt chart for the above project schedule.

$[4]$

$($b$)$ Draw a PERT diagram for the above project schedule.

$[4]$

$($c$)$ What is the earliest completion time for the project? What is the Slack Time of each task? What is the critical path of the project?

$[12]$

$($d$)$ What would happen to the project if task F was delayed by $3$ weeks?

$[2]$