he common of a major tank wars to fetermine the state of the start it would need to process up to toplications per day. It estimated that each once in process can to in mly 2011 the stond of 0.00 percent and each officer world seven hours chay, how alone would be needed to handle mat whose Round you to the whole number > The consumer loan division of a major bank wants to determine the size of the staff it would need to process up to 100 applications per day. Tt estimated that each loan officer can process a loan application in approximately 20 minutes of the utilization of loan ohi 80 (80 percent) and each one worlas seven hours each day how many officers would be needed to handle that Volume of us Round your answer to the rest Whole number Sommer
The Correct Answer and Explanation is:
To determine how many loan officers are needed to process 100 loan applications per day, let’s go step-by-step with the given data:
Given:
- Applications per day: 100
- Time per application: 20 minutes
- Working hours per officer per day: 7 hours = 420 minutes
- Utilization rate: 80% (or 0.80)
Step 1: Calculate total time required to process 100 applications
Each application takes 20 minutes, so for 100 applications: 100×20=2000 minutes needed per day100 \times 20 = 2000 \text{ minutes needed per day}
Step 2: Calculate available time per loan officer
Each officer works 7 hours/day = 420 minutes/day
However, with only 80% utilization, only 80% of that time is effectively used for processing: 420×0.80=336 effective minutes per officer per day420 \times 0.80 = 336 \text{ effective minutes per officer per day}
Step 3: Determine number of officers needed
2000 total minutes needed336 effective minutes per officer≈5.95\frac{2000 \text{ total minutes needed}}{336 \text{ effective minutes per officer}} \approx 5.95
Since we can’t have a fraction of a person, we round up to the next whole number: 6 loan officers\boxed{6 \text{ loan officers}}
Answer: 6 loan officers
300-Word Explanation:
In this scenario, the bank’s consumer loan division needs to determine how many loan officers are necessary to handle a workload of 100 loan applications per day. Each application takes approximately 20 minutes to process. That means the total daily workload is 100 × 20 = 2000 minutes.
Each loan officer works a 7-hour day, which translates to 420 minutes. However, due to administrative tasks, breaks, and other duties, officers are expected to be productive only 80% of the time. Thus, each officer effectively contributes only 80% of 420 minutes, or 336 minutes, toward application processing.
To find the number of officers required, we divide the total daily workload (2000 minutes) by the effective productive time of each officer (336 minutes). This results in approximately 5.95 officers. Because partial staffing isn’t practical in this context (you can’t hire 0.95 of a person), we round up to the nearest whole number, resulting in 6 officers.
Rounding up ensures that the workload is fully covered without overburdening staff. If only 5 officers were employed, they would collectively provide 5 × 336 = 1680 minutes, which falls short of the 2000-minute requirement. Therefore, hiring 6 officers guarantees that all applications can be processed efficiently within one workday, while maintaining a manageable workload for each employee. This calculation supports effective staffing and workload management in a high-demand environment.