Assume a computer system has $2$ CPUs with a utilization rate of $80\%$ and $90\%$ respectively. The

system has a scheduling algorithm that uses the Shortest Job First $($SJF$)$ policy. The average arrival

rate of processes in the system is $5$ processes per minute, with an average burst time of $2$ seconds

per process. Each CPU can execute a process in parallel.

a$)$ What is the total throughput of the system in processes per minute?

b$)$ What is the average response time of a process in the system?

c$)$ If the system adds another CPU, what is the new total throughput of the system assuming

the same utilization rates?

d$)$ If the utilization rate of the second CPU is increased to $95\%,$ what is the new total

throughput of the system assuming the same number of CPUs?

e$)$ Explain how the response time and throughput of a system are related and how operating

system designers balance the two when designing scheduling algorithms.