Amelio Rodriguez Computing 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 Predecessor

A

$12$

minus

B

$14$

A

C

$8$

A

D

$4$

$$B$,$ C

E

$18$

D

$$Amelio$\text{'}$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$$ places$).$Sue Helms Appliances wants to establish an assembly line to manufacture its new$$ 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

$10$

minus

B

$10$

A

C

$8$

$$A$,$ B

D

$10$

$$B$,$ C

E

$7$

C

F

$5$

$$D$,$ E

font size increased by $4$ Upper Afont size increased by $4$ Upper Cfont size increased by $4$ Upper Ffont size increased by $4$ Upper Bfont size increased by $4$ Upper Efont size increased by $4$ Upper D

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 workstationsequals

$$

$5($round your response up to the next whole$$ number$).$

Part $3$

$$b$)$ The assignment of tasks to workstations should$$ be: $($Hint: Number workstations sequentially in terms of precedence relationships and combine any applicable$$ tasks.$)$

Task

Workstation$$ #

A

$$

Station $1$

Station $3$

Station $5$

Station $2$

Station $6$

Station $4$