a$)$ Given in the following table are the task necessary for the assembly of Fine Cedar Chest, the length of the time needed to perform each task, and the operations that must be completed prior to subsequent operations.

Work Element Precedence Time $($min$)$

A None $2$

B A $4$

C B $5$

D None $5$

E D $3$

F None $1$

G F $2$

H C$,$ E$,$ G $4$

i$)$ Calculate the cycle time needed to compete $300$ cedar chests in a $35-$hour week

ii$)$ Determine the minimum number of workstations that can be use on the assembly line and still reach the production quota?

iii$)$ Balance the line and calculate the line efficiency

iv$)$ Rebalance the line with a cycle time of $9$ minutes. Determine the new minimum number of workstations output and line efficiency.