This has me a bit boggled and I even tried using the What-If Analysis in Excel to figure it out..
Statistics are these:
- A call center takes in roughly 100 calls a day
- The average time to answer the calls so far is 60 seconds
- There are 30 days in the month
- The current day of the month is 10
Is there a way to find out how many calls at what average Time to Answer in order to bring down the average from 60 seconds to 45?
Clairification Example
- Today is August 10th and so far there have been 1,000 calls
- The average Time-to-Answer so far is 60 seconds
Answer: It will take X more calls at Y (average Time to Answer) to reach an average time-to-answer of 45 seconds.
- This will range of course due to being a double variable, it will take a higher number of calls at a higher average time to answer and likewise for lower.
The relation is $$60\cdot 1000 + Y\cdot X = 45\cdot(1000+X)$$ where $X<=2000$
Therefore $Y=45-{15000\over X}\leq37.5$ seconds per call.
Also since $Y\geq0$ we know $X\geq 334$ calls.