Turner's Furniture has developed a new style of chairs that will be made on an assembly line. The schedule requires $75$ chairs in an $8-$hour day. The assembly includes seven tasks. The table below indicates the performance time and the sequence requirements for each task.

Task

Performance Time $($minutes$)$

Predecessor

A

$1$

B

$2$

A

C

$3$

B

D

$2$

B

E

$4$

C$,$ D

F

$1$

E

G

$2$

F

Based on utilizing the Longest Operating Time heuristic:

a$.$ What is the cycle time for this assembly operation?

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b$.$ What is the theoretical minimum number of workstations?

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c$.$ Where you able to balance the problem to achieve the theoretical number of stations?

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d$.$ Based on utilizing the longest operating time rule, what station should task D be assigned to$?$

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Task F$?$

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e$.$ Is there an opportunity to improve the line balance?

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$.$ If so$,$ what is the cycle time, idle time, and efficiency?

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