Stanford Rosenberg Electronics wants to establish an assembly line for producing a new$$ product, the personal digital assistant$($PDA$).$ The$$ tasks, task$$ times, and immediate predecessors for the tasks are as$$ follows:

$$

Task

Time$($sec$)$

Immediate Predecessors

A

$12$

$$

B

$15$

A

C

$7$

A

D

$5$

$$B$,$ C

E

$18$

D

$$Rosenberg$\text{'}$s goal is to produce $180$ PDAs per hour.

Part $2$

$$a$)$ The cycle time for the production of a PDA$=$ enter your response here seconds. $($Round your response to two decimal$$ places.$)$

Part $3$

$$b$)$ The theoretical minimum number of workstations that Rosenberg can achieve in this assembly line$=$ enter your response here. $($Round your response up to the next whole$$ number.$)$

Part $4$

$$c$)$ For one to assign the tasks to the actual workstations and be able to use the$$ "theoretical minimum"$$ number, the activity assignment should$$ be: