Team Computer Project. Consider a situation $($factory$)$ where there is a limit

of $4$ jobs allowed at any time; arrivals to a full system are lost. Assume that all interarrival and processing times are exponentially distributed with mean rates specified.

Job processing has two steps $($Step $1$ uses Machine $1$ and Step $2$ uses Machine $2).$

That is$,$ there are two independent processing steps that must be done in the sequence: Machine $1$ then Machine $2.$ The system is automated with$-$respect$-$to job

movement between the queue and machines and between machines and then from

the last machine to shipping $($not part of this problem$).$ There currently is no space

for a job to wait for processing at Machine $2$ after it has completed processing at Machine $1.$ Therefore, the completed job is left on Machine $1$ until Machine $2$ becomes

available.

Management would like to improve the factory throughput and they are want

to know what throughput improvement could be gained if they would invest in a