SECTION B

vi$)$ You are managing a construction project with the following activities,durations$($in days$),$ and precedence relationsips:

$\backslash$table$[[$Activity$,$Duration$($Days$),$Predecessor$($s$)],[$A$,5,$None$],[$B$,3,$A$],[$C$,7,$A$],[$D$,4,$B$],[$E$,8,$B$,$C$],[$F$,6,$C$],[$G$,2,$D$],[$H$,9,$E$,$F$],[$I$,4,$G$],[$J$,5,$H$],[$K$,3,$E$,$F$],[$L$,7,$G$,$K$],[$M$,6,$I$],[$N$,5,$L$],[$O$,4,$M$,$N$],[P,3,$O$],[Q,7,$N$,$O$],[R,5,$P$,$Q$]]$

a$)$ Draw the Activity on Arrow$($AOA$)$ network diagram$-$Ensure each node is properly labeled with the early start$($ES$)$and latest start $($LS$)$ times$(15$ marks$)$

b$)$ D$)$Calculate the critical path using forward and backward pass$(10$ marks$)$

ii$)$ Determine the total project duration for the critical path$(10$ marks$)$

c$)$ Suppose the Activity E is delayed by $3$ days, making its new duration $11$ days:

i$)$Recalculate the critical path and total project duration $(10$ marks$)$

ii$)$ Does this change cause any previously non critical activities to become critical?$(5$ marks$)$