Dr$.$ Lori$$ Baker, operations manager at Nesa$$ Electronics, prides herself on excellent$$ assembly$-$line balancing. The$$ assembly$-$line activities$$ are:

$$

Task

Performance

Time$($mins$)$

Predecessors

Task

Performance

Time$($mins$)$

Predecessors

A

$44$

minus$$

G

$55$

F

B

$66$

minus$$

H

$77$

$$D$,$ E

C

$88$

A

I

$22$

H

D

$77$

$$A$,$ B

J

$88$

E

E

$33$

B

K

$22$

$$G$,$ I, J

F

$44$

C

$$a$)$ For the given daily $(2424-$hour$)$ production rate of $120120$units$,$ the highest allowable cycle time$=1212$ minutes $($enter your response as a whole number$).$

$$b$)$ If the cycle time is given as $1010$minutes$,$ then the effective daily $(2424-$hour$)$ production rate$=144144$ units $($enter your response as a whole number$).$

$$c$)$ For the given $1010-$minute cycle$$ time, the theoretical minimum number of workstations$=66($round your response up to the next whole$$ number$).$

$$d$)$ The correct precedence relationship with one of the possible assignments of tasks to workstations for the given $1010-$minute cycle time is shown in

Fig. $1$

$.$

font size increased by $4$ Upper AA font size increased by $4$ Upper GG font size increased by $4$ Upper HH font size increased by $4$ Upper BB font size increased by $4$ Upper CC font size increased by $4$ Upper DD font size increased by $4$ Upper JJ font size increased by $4$ Upper II font size increased by $4$ Fig. $1$Fig. $1$ font size increased by $4$ Upper FF font size increased by $4$ Upper EE font size increased by $4$ Upper KK

x y graph

font size increased by $4$ Upper AA font size increased by $4$ Upper GG font size increased by $4$ Upper HH font size increased by $4$ Upper BB font size increased by $4$ Upper EE font size increased by $4$ Upper CC font size increased by $4$ Upper JJ font size increased by $4$ Upper II font size increased by $4$ Fig. $2$Fig. $2$ font size increased by $4$ Upper FF font size increased by $4$ Upper DD font size increased by $4$ Upper KK

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font size increased by $4$ Upper AA font size increased by $4$ Upper GG font size increased by $4$ Upper HH font size increased by $4$ Upper BB font size increased by $4$ Upper CC font size increased by $4$ Upper DD font size increased by $4$ Upper JJ font size increased by $4$ Upper II font size increased by $4$ Fig. $3$Fig. $3$ font size increased by $4$ Upper FF font size increased by $4$ Upper EE font size increased by $4$ Upper KK

x y graph

$$e$)$ The operating efficiency of the assembly line $=93\mathrm{.}3393\mathrm{.}33\%($enter your response as a percentage rounded to two decimal $$places$).$

$$f$)$ The idle time for the assembly line per cycle$=44$ minutes $($enter your response as a whole$$ number$).$