Suppose the part in the previous problem $($Q $3\mathrm{.}18,$ see it below$)$ is made in very large quantities on a production line in which an automated work handling system is used to transfer parts between stations. Transfer time between stations is $15$ sec$.$ Total time required to set up the entire line is $150$ hours. The operation times at the individual stations remain the same as in the previous problem. Determine $($a$)$ manufacturing lead time for a part coming off the line, $($b$)$ production rate for operation $3,($c$)$ theoretical production rate for the entire production line. $($d$)$ How long would it take to produce $10,000$ parts after the setup has been completed? $($e$)$ Given the cycle times for the individual stations, determine the average station utilization on the line.