$3\mathrm{.}19$ Suppose the part in the previous problem 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 $15sec.$ Total time required to set up the entire line is $150hr.$ The operation times at the individual stations remain the same as in the previous problem. Determine the $($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 arverage station utilization on the line.