Suppose parcels follow an M$/$M$/1$ queueing model with a mean inter$-$arrival time of $30$ seconds $(0\mathrm{.}5$ minutes$)$ and a mean service time of $24$ seconds $(0\mathrm{.}4$ minutes$).$Part I $(80$ points$)$Determine the:$1)$ The value of the arrival rate $2$ and the service rate u and specify the units,$2)$ Determine the utilization factor,$3)$ Find the average waiting time in the queue for one parcel, $4)$Find the average number of parcels waiting in the queue,$5)$ Determine the average total number of parcels in the system,$6)$ What if the probability that the system is empty?$7)$What is the probability that there are $3$ parcels in the system?$8)$ The service provider will shut down the service operation if the probability that the system is idle more than $30\%.$ Will it shut down?Suppose one seeks to have the utilization factor at $95\%,9)$ Propose one way to change the arrival rate value to reach that objective,$10)$ Will the probability of the system being idle increase or decrease? Justify your answer.