On average, after the execution of task CT$1,\backslash (20\backslash \%\backslash )$ of all applications are rejected. Meanwhile, task CT$2$ leads to $\backslash (30\backslash \%\backslash )$ of further rejections. If either of the checks has an unsatisfactory result, the application is rejected $($task AW$).$ The arrival process is Poisson with an average arrival of $5$ cases per hour during business hours. For each task, exactly one dedicated resource is available. The processing time of every task follows an exponential distribution. The mean processing times for tasks CT$1,$ CT$2,$ AC$,$ and AW are respectively $\backslash (5,4,3\backslash ),$ and $3$ min $.$ The wage of each resource is e $20$ per hour. Business hours are from Monday to Friday from $9$ a$.$m$.$ to $5$ p$.$m$.$ Resources are only available during these hours.

a$.$ Determine the resource utilization of each resource.

b$.$ Determine the average cycle time of the process.

c$.$ Determine the cycle time efficiency of the process.

d$.$ Determine the average number of mortgage applications that are being handled at any given point in time.

Hint For this exercise, it might be convenient to use a combination of process simulation, Little's law, and flow analysis.