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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.
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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.

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  • $\begingroup$ This was exactly what I needed.. Thanks!! $\endgroup$
    – Podis
    Aug 10, 2020 at 17:35

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