A dress$-$making operation is being designed as an assembly line. Following table shows the tasks that need to be performed, their task times, and preceding tasks. If the goal is to produce $30$ dresses per hour, answer the questions that follow the table. $(20$ points$)$

$\backslash$table$[[$Work Element,Immediate Predecessor,Task Time $($sec$)],[$A$.$ Cut dress body,None,$30],[$B$.$ Cut sleeves,None,$40],[$C$.$ Cut collar,None,$20],[$D$.$ Sew dress body,A$,100],[$E$.$ Sew sleeves to dress,B$,$ D$,25],[$F$.$ Sew collar to dress,C$,$ D$,50],[$G$.$ Hem dress,D$,$ E$,$ F$,50],[$H$.$ Package dress,G$,90]]$

a$)$ Compute the cycle time.

b$)$ Which task is the bottleneck?

c$)$ What is the maximum output for this line?

d$)$ Compute the theoretical minimum number of stations.

e$)$ Assign work elements to stations, using the longest task time rule.

Compute the efficiency and balance delay of your assignment.