$1.$ Deacon Systems assembles and sells high power and expensive servers for financial service organizations. The office in Winston Salem is relatively small and consists of $5$ people who process and approve loans for financing customer purchases. The office serves both customers located in New York and customers located in Charlotte, NC$.$ The interarrival time between loans coming from New York $($NY$)$ is exponentially distributed with a mean of $6$ hours and the interarrival time between loans arriving from Charlotte is exponentially distributed with a mean of $8\mathrm{.}5$ hours. The first step in processing the loan applications is Evaluation and Analysis. There are two Evaluation and Analysis employees $$ one dedicated to processing applications from New York and one dedicated processing applications from Charlotte. After Evaluation and Analysis, the loan goes to an employee that determines the interest rate. There is only one employee that does the Interest Rate Determination and thus this employee processes loans from both New York and Charlotte. The final step is to determine the Loan Terms. Like the Evaluation and Analysis work, there is a single employee that does the Loan Terms for the applications from New York and another employee that does the Loan Terms for the loans from Charlotte. Deacon has collected a great deal of processing time data and based on an analysis of this data has estimated the processing times at the three stages as shown in the table below. Deacon Systems divides the calendar year into $4$ quarters each of $13$ weeks. It operates $9$ hours per day, $5$ days per week.

Processing Time Data $($triangular distribution, hours$)$

Process Step Processing Time

Evaluation and Analysis $2\mathrm{.}4,3\mathrm{.}1,5\mathrm{.}8$

Interest Rate Determination $0\mathrm{.}4,0\mathrm{.}6,1\mathrm{.}0$

Loan Terms $4\mathrm{.}4,5\mathrm{.}6,7\mathrm{.}3$

Develop a simulation model for Deacon Systems and run it for one quarter. Based on replicating the model one time, use the results from your simulation run to complete the table on the next page. Use hours for the units where your answer corresponds to a time and enter all answers with $2$ digits to the right of the decimal point. $(60$ points$)$

Performance Measure Value$($s$)$

Average Time in System for Loan Applications from Charlotte

Average Time in System for All Loan Applications

Minimum and Maximum Time a Loan Spent in the System

The Average Amount of Time a Loan from NY had to wait for the Evaluation and Analysis Employee

The Minimum and Maximum Amount of Time a Loan from NY had to wait for the Evaluation and Analysis Employee

The Utilization of the Employee that Performed the Evaluation and Analysis of Loans from Charlotte

The Utilization of the Employee that Performed the Evaluation and Analysis of Loans from NY

The Utilization of the Employee that Performed the Interest Rate Determination

The Average Number of Loans that Arrived from NY Waiting for the Loan Terms Employee

The Minimum and Maximum Number of Loans that Arrived from NY Waiting for the Loan Terms Employee