In the pictured assembly line, numbers indicate time in seconds. It is known that for a particular production setup the cycle time is $112$ seconds. Answer the following questions:

$($i$)$ What would be the throughput $($output rate$)$ of the process per workday $(8-$hour workday$)$ with such cycle time?

$($ii$)$ For that particular production setup, what would be the theoretical minimum number of workstations?

$($iii$)$ If you balance the line for the needed cycle time using the $$longest task time first$$ rule, what would be the total idle time?

$($iv$)$ What would be the line balance delay after such balancing?