A facility is trying to set up an assembly line, and has identified the various tasks, and their relationship to each other, as shown in the following table. Managers wish to produce $600$ units per day, working two $8-$hour shifts.

$\backslash$table$[[,],[$TASK$,$PRECEDING TASK,$\backslash$table$[[$TIME TO$],[$PERFORM $($SEC$)]],],[$A$,-,20,],[$B$,-,30,],[$C$,-,25,],[$D$,-,10,],[$E$,$A$,55,],[$F$,$D$,$ B$,$ C$,30,],[$G$,$E$,25,],[$H$,$F$,$ G$,40,],[,,,]]$

$\backslash$table$[[,,],[,,$Total$]]$

$235$

a$.$ What is the cycle time? $[$Blank$1]$ seconds

$96$

b$.$ What is the theoretical minimum number of workstations? $[$Blank$2]$

c$.$ By balancing the line based on longest processing time, what are the actual number of stations? $[$Blank$3]$

d$.$ Is there an improved cycle time? $[$Blank$4]$

$$

$33$

$34$

$35$

$36$

$37$

$38$

$39$

$0$

$1$

$2$

g$.$ Based on your answer to d$.,$ what is the total actual idle time at all workstations over the course of the two $8$ hour shifts $($minutes$)?[$Blank$7]$

check and fix all of the above.