$\backslash$table$[[$ACTIVITY$,$DURATION $($WEEKS$),$PREDECESSORS$],[$A Hire workers,$8,$None$],[$B Install equipment,$6,$None$],[$C Order materials,$3,$None$],[$D Test equipment,$4,$B$],[$E Train workers,$6,$A$,$ B$],[$F Run pilot tests,$5,$C$,$ D$]]$

a$.()$ Identify all the critical activities and path$($s$).$ How long will the entire project take?

c$.(**)$ Suppose management of Spartan Cabinets has developed additional