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# Question:Problem 1 Customers arrive at a bank drive-up window every 12 minutes based on a Poisson distribution.

**Question:Problem 1**

Customers arrive at a bank drive-up window every 12 minutes based on a Poisson distribution. Once they arrive at the teller, service time is exponentially distributed based on a rate of 6 minutes per transaction,

a. What is the probability that 3 or fewer customers will arrive in one hour?

b. How many customers are most likely in line (waiting) at any one point in time?

c. What will be the average time waiting in the system?

d. What will be the average time in the system?

**Problem 2**

Peri Thompson is the sole dispatcher for Thompson Termite Control. Peri's job is to take customer calls, schedule appointments, and assist with billing issues over the phone. Peri can handle on average 25 calls per hour.

a) Typically, Peri gets about 20 calls an hour. Under these conditions, what is the average number of customers waiting, and what is the average waiting time?

b) Monday morning are unusually busy and Peri receives an average of 23 calls per hour during those peak times. Recalculate the average number of customers waiting and the average waiting time. What would you suggest if business takes off and Peri's average increases to 23 calls per hour all of the time?

**Problem 3**

The Lenovo Refurbishing Center repairs used laptops that are returned under warranty.

- The center receives and processes, on average, 50 laptops per day
- All laptops are tested upon receipt: 40% are immediately rejected, and the remaining 60% are sent to the refurbishing area
- On average, there are 15 laptops in the testing area waiting or being worked on
- On average, there are 11 laptops in the refurbishing area waiting or being worked on

A) What is the average throughput time for all laptops entering the system

B) What is the average throughput time for a laptop that goes through both testing and refurbishing? Suppose Lenovo wants this time to be less than one day. Are they currently meeting this performance goal?

**Problem 4**

ABS sells construction materials to commercial and home builders. One of ABS's key processes is the order fulfillment process shown below and described as follows:

- All orders are assessed on arrival. The typical order spends 0.25 days in this order assessment step before moving on.
- Of the orders, 30% are immediately declined for various reasons and have no processing time.
- 20% of all orders are large orders. Average total time in this large orders processing step, including waiting and actual process time, is 2 days.
- 50% of all orders are small orders. Average time in this small orders processing step, including waiting and processing time, is 0.5 days.
- ABS receives an average of 20 order requests a day. The system is currently in steady state.

A) What is the estimated total inventory for the entire order fulfillment process?

B) Based on the information given earlier and your answer to part a, what is the estimate total throughput time for the average order entering the process?