Problem $2.(22$ points$)$

A manufacturer needs to produce $240$ coffee pots per $8-$hour day. The tasks required to produce a coffee pot have been identified, timed in seconds, and ordered as indicated in the table.

$\backslash$table$[[$Task$,$Time,Predecessors$],[$A$,80,--],[$B$,25,$A$],[$C$,35,$A$],[$D$,20,$B$,$ C$],[$E$,50,$C$],[$F$,70,$E$],[$G$,45,$D$],[$H$,25,$G$],[$I$,15,$G$],[$J$,60,$F$,$ H$,$ I$]]$

a$.$ Draw the precedence diagram. $(5$ points$)$

b$.$ What is the workstation cycle time required to produce $240$ units per day? $(2$ points$)$

c$.$ Balance this line using the longest task $($processing$)$ time rule. Use largest number of following tasks $($most following tasks$)$ as a secondary $($tiebreaker$)$ rule. You need to show all the assignments to the workstations and the order in which you assign tasks. $(10$ points$)$

d$.$ What is the efficiency and percent idle time for the balanced line? $(5$ points$)$