Question $1$: $(50$ pnt$.)$

Calculate the expected duration for each activity in Table $1$ using the PERT formula:

$($Optimistic $+4^{**}$ Most Likely $+$ Pessimistic$)/6(12$ pnt$)$

Draw the network as AON $(10$ pnt$)$

Determine the critical path of the project. $(5$ pnt$)$

Calculate the early start $($ES$),$ early finish $($EF$),$ late start $($LS$),$ and late finish $($LF$)$ for each activity. $(10$ pnt$)$

Calculate the slack time for each activity. $(8$ pnt$)$

What is the expected completion time of the entire project? $(5$ pnt $)$

Show all your work and explain your reasoning for each step.

Table $1-$ Question $1$

$\backslash$table$[[$Activity$,$Description,Optimistic Time $($day$),$Most Likely Time $($day$),$Pessimistic Time $($day$),\backslash$table$[[$Preceding$],[$Activities$]]],[$a$,$Site Preparation,$10,14,18,$None$],[$b$,$Environmental Assessment,$7,10,13,$None$],[$C$,$Foundation Work,$15,20,25,$None$],[$d$,$Structural Framing,$22,28,34,$C$],[$e$,$Roofing,$8,12,16,$d$],[$f$,$Exterior Walls,$12,15,18,$d$],[$g$,\backslash$table$[[$Electrical$],[$Rough$-$in$]],10,13,16,$c$,$ d$],[$h$,\backslash$table$[[$Plumbing$],[$Rough$-$in$]],9,12,15,$c$,$ d$],[$i$,\backslash$table$[[$HVAC$],[$Installation$]],11,14,17,$d$,$ e$],[$j$,$Interior Finishing,$18,22,26,$e$,$ f$,$ g$,$ h$,$ i$],[$k$,$Final Inspections and Handover,$5,7,9,$j$]]$