An assembly line to be balanced has six tasks in precedence. The task times are shown in the following table. Based on demand forecasts, the output rate has to be $160$ units per day. The line operates $8$ hours a day. Compute the theoretical minimum amount of idle time $($I$).$

Tasks Immediate Predecessor Task Time in Minutes

A NONE $3$

B A $1$

C A $2$

D B$,$ C $3$

E C $3$

F D$,$ E $2$

Question $9$ options:

$0$

$1$

$2$

$3$