$(30$ points$)$ Calculation questions:

$32.(30$ points$)$ Consider the Amrolife project in the American Royal Financial case study, please conduct the following analysis

$\backslash$table$[[$Index$,$Tasks,$\backslash$table$[[$Immediate$],[$Predecessors$]],\backslash$table$[[$Duration$],[($In week$)]]],[$A$,$Market Research,$-,8],[$B$,$Cost Analysis,$-,4],[$C$,$Product Design,A$,$B$,12],[$E$,$Development Analysis,C$,10],[$F$,$Developing Product Model,D$,8],[$G$,$Filing Contracts,E$,12],[$H$,$Product Testing,E$,10],[$I$,$Pales$/$Marketing Planning,E$,8],[$S$,$Sales Force Training,F$,$I,$6]]$

$($a$)(5$ points$)$ Draw the network representation $($AON$).$

$($b$)(10$ points$)$ Calculate the earliest and latest starting$/$finishing times $($ES$/$EF$/$LS$/$LF$)$ of each activity.

$($c$)(5$ points$)$ Calculate slack time of each activity.

$\backslash$table$[[$Activity$,$Duration,Predecessor,ES$,$EF$,$LS$,$LF$,$Slack$],[$A$,8,-,,,,,],[$B$,4,-,,,,,],[$C$,12,$A$,$B$,,,,,],[$D$,10,$C$,,,,,],[$E$,8,$D$,,,,,],[$F$,12,$E$,,,,,],[$G$,10,$E$,,,,,],[$H$,8,$E$,,,,,],[$I$,6,$G$,$H$,,,,,],[$J$,4,$F$,$I,,,,,$]]$

$($d$)(5$ points$)$ Identify the critical activities, non$-$critical activities and their slacks.

$($e$)(5$ points$)$ Identify the critical path and the minimum project duration.