A manufacturing plant called ProMakers, there's an effort to streamline the production process for a specific product. The goal is to create $80$ items every hour. The details reveal the different steps involved in putting together these products as follows.

a$.$ Determine the cycle time that will meet this level of demand.

b$.$ Determine how many workstations are needed to balance this line to maximum efficiency.

c$.$ What is the total idle time for an eight$-$hour workday?

$\backslash$table$[[$Work Element,Time $($Sec$),$Immediate Predecessor$($s$)],[$A$,40,-],[$B$,36,$A$],[$C$,20,$A$],[$D$,25,$A$],[$E$,30,$B$,$ C$],[$F$,34,$D$],[$G$,35,$E$],[$H$,5,$F$],[$I$,15,$E$,$ H$],[$J$,40,$H$],[$K$,38,$G$,$ I, J$]]$