Sue Helms Appliances wants to establish an assembly line to manufacture its new$$ product, the Micro Popcorn Popper. The goal is to produce five poppers per hour. The$$ tasks, task$$ times, and immediate predecessors for producing one Micro Popcorn Popper are as$$ follows:

$$

Task

Performance Time$($mins$)$

Task Must Follow Task Listed Below

A

$10$

$$

B

$12$

A

C

$9$

$$A$,$ B

D

$9$

$$B$,$ C

E

$8$

C

F

$4$

$$D$,$ E

ACFBED

In the diagram, there are $6$ circles labeled using the letters from A to F$.$ There are $8$ of arrows, and each arrow connects one circle to another circle. The arrows are situated in the following manner: A to B$,$ A to C$,$ B to C$,$ C to D$,$ B to D$,$ C to E$,$ D to F$,$ and E to F$.$

Part $2$

$$a$)$ The theoretical minimum number of workstations$=$enter your response here $($round your response up to the next whole$$ number$).$