$7.$ ?Dr $.$ ?Gretchen Unger, operations manager at BC Electronics, prides herself on running a most efficient assembly line. She has been told the firm needs to complete $96$ ?instruments per $24-$ hour day. Here are the activities that make up an instrument:

Task Time Predecessors

A $3-$

B $6-$

C $7$ ? A

D $5$ ? A $,$ ?B

E $2$ ? B

F $4$ ? C

G $5$ ? F

H $7$ ? D $,$ ?E

I $1$ ? H

J $6$ ? E

K $4$ ? G $,$ ?I, J

? $50$

a $).$ ? Draw the precedence diagram.

b $).$ ? What is the highest allowable cycle time?

c $).$ ? If the cycle time is given as $10$ ?minutes, what is the daily $(24-$ hour $)$ ?production rate?

d $).$ ? With a $10-$ minute cycle time, what is the theoretical minimum number of work stations with which the line can be balanced?

e $).$ ? With a $10-$ minute cycle time and six workstations, what is the efficiency?

f $).$ ? What is the total idle time per cycle with a $10-$ minute cycle time and six work stations?

g $).$ ? What is the best work station assignment you can make without exceeding a $10-$ minute cycle time and what is the efficiency? $(13$ ?points $)$