P$1$ has a production rate of $15$units$/$hour$,$ P$2=30$units$/$hour$,$ P$3=10$ units per$$ hour, P$4=4$units$/$hour$,$ P$5=1$unit$($s$)$ per hour for each P$5$ and P$6=5$ units per hour.

Operation P$4$ occurs seperately from and simultaneously with operations$$ P$1-$P$3.$

Operation P$5$ has three parallel and identical$$ lines; therefore, each part only needs to go through one of the three lines.

$$a$)$ The bottleneck of this system is station P

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$$b$)$ The bottleneck time of the system is

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enter your response here minutes per unit.

$$c$)$ The throughput time is

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enter your response here minutes per unit.