The arrival rate to a machining center is $15$ parts per hour and the machining center takes an

average of $2$ minutes to process each part. Assume part arrivals and processing times are

variable with $$

$2=1$ and $$

$2=2.$ Also assume that the part arrival and service processes

follow a general distribution.

$($a$)$ What is average utilization?

$($b$)$ What is the average length of the queue? What is the overall average level of work$-$inprocess inventory?

$($c$)$ What is the average cycle time?

$($d$)$ What is average throughput?

$($e$)$ The machining center feeds into an assembly workstation as described in the following

figure. What is the coefficient of variation in the arrival process of the assembly

workstation?