Q$3(20$ points$)$ The project information is given below $($under normal conditions, in weeks$).$

A$.(6$ points$)$ Under normal conditions, which path is the critical path, and what is the project duration? Please use two$-$pass $($forward$/$backward pass$)$ method $(3$ points for the two$-$pass method, $2$ points for the critical path, $1$ point for project duration.$)$

Critical Path$($s$)$: $q,$

Project Duration:

$\_($don$\text{'}$t forget time units!$)$

B$.(2$ points$)$ Suppose Jack, the only employee responsible for activity C wants to take a two$-$week vacation during weeks $3$ and $4.$ Can you allow Jack to take the vacation and still complete the project without delay? Briefly justify your answer.

C$.(2$ points$)$ Suppose that activities B$,$ C$,$ E$,$ F$,$ and I can be crashed. The normal time, crash time, normal cost and crash cost are shown in the table below. What is the weekly crash cost of each activity? $($Crash time is the shortest possible activity time and crash cost is the cost associated with the crash time$)$

$\backslash$table$[[$Activity$,\backslash$table$[[$Normal Time$],[($weeks$)]],\backslash$table$[[$Normal Cost$],[($$$)]],\backslash$table$[[$Crash Time$],[($weeks$)]],\backslash$table$[[$Crash Cost$],[($$$)]],\backslash$table$[[$Weekly Crash Cost$],[($$$/$week$)]]],[$B$,10,140,6,240,],[$C$,7,320,5,420,],[$E$,2\mathrm{.}5,400,1\mathrm{.}5,440,],[$F$,7,250,3,290,],[$I$,2,170,1,200,]]$

D$.(10$ points$)$ Suppose the management instead wants the project to be completed in $14$ weeks. How can you achieve this goal at minimum cost? Please report your crashing steps in the table below. $($The table size does not imply number of steps.$)$

$\backslash$table$[[\backslash$table$[[$Project Duration$],[($weeks$)]],$Critical Path$($s$),\backslash$table$[[$Crashable Tasks on Critical Paths$]],\backslash$table$[[$Best Option$],[[$weeks to$],[$crash$]]]],[,,,],[,,,]]$