You are asked to perform a capacity analysis for a bank. The current resources of the bank are as follows:

Resources Number of Service Providers Processing Time $($min$)$

Drive$-$through $43$

Teller $410$

ATM $35$

Specialist $220$

In addition, the following information is presented to you on the operations of the bank.

a$)$ On average, $50\%$ of the customers use the drive$-$through lanes without leaving their cars.

Customers can perform tasks such as making a withdrawal, paying bills, or depositing a check via

the drive$-$through lanes. There are $4$ identical drive$-$through lanes currently operating and the

average processing time of a customer is $3$ minutes in each of these lanes.

b$)$ On average, $80\%$ of the customers who walk into the bank prefer talking to a bank teller and the

remaining $20\%$ prefer the ATM, which is located inside the store. There are $4$ bank tellers and

each of them services a customer in $10$ minutes on average. There are $3$ ATMs, and it takes $5$

minutes on average for a customer to complete service via ATM.

c$)$ After talking to a bank teller, $20\%$ of the customers are directed to a specialist because the bank

tellers cannot perform operations such as opening a new account or applying for a credit card.

There are $2$ specialists in the bank, and it takes an average of $20$ minutes for a specialist to

complete the service for a customer.

The above description of processes is provided as a diagram below for convenience. The number of

service providers per resource and processing time are given in each diagram block.

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The manager of the bank is interested in the following questions:

a$)$ What is the capacity of each resource in the bank $($drive$-$through lanes, tellers, ATM, and

specialist$)$ in number of customer$-$arrivals per hour?

b$)$ What is the system capacity of the bank in number of customer$-$arrivals per hour? Identify the

bottleneck$($s$).$ What is the slack of each resource in total number of customer $-$arrivals per hour?

c$)$ If the bank can add two additional unit of resource per bottleneck resource$($s$),$ what would be the

new system capacity and bottleneck$($s$)?$