Question

A bank receives load applications from 6 customers a day. The bank has promised customers that applications will be processed in the order they are received. The table below shows the applications in the order they were received, the processing time for each loan application, and the due date that customers need to hear about their application status: Customer Processing time (days) Due date (days) A 9 12 B 11 17 C 8 10 D 7 12 E 10 21 F 12 27

a. Determine the average processing time for applications, the average days tardy for each customer's application, and the average number of applications being processed if the bank processes the applications in the order they were received. (Round your answers to 2 decimal places.)

Answer 1

The average processing time for the loan applications is 9.50 days. The average days tardy for each customer's application is 16.33 days, and given the sequential nature of the processing, the average number of applications being processed at any time is 1.

Step-by-step explanation:

To calculate the average processing time for the loan applications, we add the processing times for all customers and divide by the number of customers:

(9 + 11 + 8 + 7 + 10 + 12) / 6 = 57 / 6 = 9.50 days.

The average processing time for applications is therefore 9.50 days.

To compute the average days tardy for each customer's application, we need to determine if the processing time exceeds the due date for each customer. If the processing starts on Day 1 for the first customer and follows consecutively without interruption, the cumulative processing days would be 9, 20 (9+11), 28 (20+8), 35 (28+7), 45 (35+10), and 57 (45+12). Now we compare these with their respective due dates to find the tardiness:

• Customer A: 0 days tardy (processed on Day 9, due on Day 12)
• Customer B: 3 days tardy (processed on Day 20, due on Day 17)
• Customer C: 18 days tardy (processed on Day 28, due on Day 10)
• Customer D: 23 days tardy (processed on Day 35, due on Day 12)
• Customer E: 24 days tardy (processed on Day 45, due on Day 21)
• Customer F: 30 days tardy (processed on Day 57, due on Day 27)

To calculate the average days tardy, we add these values and divide by the number of customers:

(0 + 3 + 18 + 23 + 24 + 30) / 6 = 98 / 6 = 16.33 days.

The average number of days tardy for each customer's application is 16.33 days.

To determine the average number of applications being processed at any given time, we would consider the overlap in processing times. However, since the question specifies that applications are processed in the order they were received without specifying any capacity constraints or parallel processing, we could imply that no more than one application is ever being processed simultaneously, assuming they are processed sequentially without any delay in between. Thus, the average number of applications being processed would be 1.