$1)$ A steel manufature company has a production line that consists of four workstation $.$ the tasks $,$their times, precedence relantionship shown below :

Task Times $($ minutes$)$ Immediate Predecessors

A $10-$

B $15$ A

C $20$ A

D $25$ B

E $30$ B

F $35$ C$,$D

The company operates $8$ hour per day and needs to produce $20$ units per day. Calculate the following $$

$1.$ What is the cycle time for line?

$2.$ What is the theoretical minimum number of workstation?

$3.$ Propose a balance line that minimize idle time. what is the efficiency of your line?