Based on the following activity precedence relationship a$)$ Draw the AON and CPM $($Critical Path Method or AOA $-$ Activity on Arrow$)$ network. Clearly label the activities, dummy activities, events, nodes, edges etc. $($if any$)$ and follow the network rules; b$)$ Perform forward and backward path calculations including total float, free float, interfering float, and independent float, and clearly show the critical path; c$)($BONUS$)$ Assuming one $($or many$)$ activities are delayed, is it possible that there will be two or three critical paths? If yes, at what durations, if no$,$ why?

Formula:

$TF=LF-EF=LS-ES,FF=E{S}_{\text{s}\text{u}\text{c}\text{c}\text{e}\text{s}\text{s}\text{o}\text{r}\text{a}\text{c}\text{t}\text{i}\text{v}\text{i}\text{t}\text{i}\text{e}\text{s}}-E{F}_{\text{a}\text{c}\text{t}\text{i}\text{v}\text{i}\text{t}\text{y}}\frac{?}{\text{I}}$

$ntF=TF-FF$ IndF $=$min$(E{S}_{\text{s}\text{u}\text{c}\text{c}\text{e}\text{s}\text{s}\text{o}\text{r}\text{a}\text{c}\text{t}\text{i}\text{v}\text{i}\text{t}\text{i}\text{e}\text{s}}-L{F}_{\text{a}\text{c}\text{t}\text{i}\text{v}\text{i}\text{t}\text{y}})$

$\backslash$table$[[$Activity$,$Predecessors,Duration $($in days$)],[$A$,-,5],[$B$,-,2],[$C$,-,4],[$D$,$A$,2],[$E$,$A$,$B$,5],[$F$,$A$,$B$,$C$,3]]2$