Consider a two$-$station serial production line. The rst station consists of a single

machine with a mean processing time of $3$ hours and a standard deviation of $9$ hours. At the

second station, there are two identical machines, each with a mean and standard deviation

of $5$ hours and $2$ hours, respectively, for the processing time.

a$)($ pts$)$ What is the highest arrival rate that this system can handle?

b$)($ pts$)$ Using analytical approximations, calculate the average cycle time for the system

assuming that the inter$-$arrival process is exponential with a rate of $0$:$25$ jobs$/$hour$.$

c$)$ pts$)$ Suppose the two machines in the second station is replaced by a single machine

that is twice faster such that the mean process time is $2$:$5$ hours. Assume that the

standard deviation stays the same. How will the CT change? Show your calculations

clearly. Compare the cycle times in parts b$)$ and c$)$ and explain the reason$($s$)$ for the

dierence.

d$)($ Suppose that the production line in part b$)$ is reversed so that station $2$ replaces