Question$-1$:

First shift employees at General Motors work from $6$am to $2pm$ Monday through Friday. Everyone on the assembly line is allowed a $30$ minute lunch and two $20$ minute breaks, but other cross$-$trained associates cover lunches and breaks for the associates on the assembly line so the line doesn't stop. The processes of the assembly line have the following dependencies:

$\backslash$table$[[$Task$,$Average Time $($Seconds$),$Predecessor$],[$A$,45,$None$],[$B$,90,$None$],[$C$,110,$A$],[$D$,120,$B$],[$E$,70,$D$],[$F$,120,$C$],[$G$,115,$E$],[$H$,120,$F$,$ G$]]$

The Plant Manager needs first shift to achieve an output of $100$ cars.

a$)$ Compute the desired & current Takt time for the line

b$)$ What is the theoretical minimum number of workstations?

c$)$ Draw the precedence diagram, and then create work stations. Follow the "greatest positional weight" heuristic rule to assign these tasks to the work stations. Show which tasks are assigned to each workstation.

d$)$ Compute the line efficiency & ratio

e$)$ What is the maximum output that could be achieved by a single assembly line in $8$ hours?