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Question

If a call center answers 6,000 calls a month and each calls takes 3 minutes to answer on average, how many people would it take to answer these calls, if each individual is working 6 hours a day. There are 23 working days in the month. In addition, how many persons would it take to annswer the 6,000 calls in a minute

Submitted: 290 days and 14 hours ago.
Category: Math
Value: $15
Status: CLOSED
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Already Tried:
A call center receives 9,945 calls in the month of August, (a 23 day period). The total number of seconds used to answer these calls was 1,709,997 which is an average of 172 seconds per call or 3 minutes per call.

Question - How many service associates would it take to answer the 9,945 calls if a working day is 21,600 seconds or 360 minutes and there are 23 working days each month.

And How many associates would it take to answer the same number of calls in 23 days if each call was answered in on minute. (It took a minute to answer the call).

Posted by Fermat 290 days and 12 hours ago.

Answer

6000 calls/month becomes
72,000 calls/year, which is equivalent to
216,000 mins/year (at 3 mins per call)
======

12 months at 23 days/month = 276 days/yr
Each employee works 6 hrs/day
time to be worked by each employee is 1,656 hrs/yr
or,
99,360 mins/yr
=====

Therefore number of employees required = 216,000/99,360 = 2.174
i.e. number of employees = 3 employees

Answer:3 employees
==============

Check
3 employees work 18 hrs/day = 1,080 mins/day
3 employees work 1,080*23 = 24,840 mins/month
3 employees work 24,480*12 = 298,000 mins/yr

which covers the amount of call time required, i.e. 216,000 mins


You also asked,

In addition, how many persons would it take to annswer the 6,000 calls in a minute.

This is impossible, since each call takes 3 mins to answer, it would be impossible to answer any one call in 1 minute

Edited by Fermat on 2/5/2009 at 9:30 PM

290 days and 11 hours ago.

Reply

Hello: I like your first answer it corresponds with mine, however, I would still like you to attempt the second part of the question.

 

Say for argument sake that each of the 6000 calls was answered in a minute how many people would it take to answer these calls, based on your formula, are you saying it would take .72 of a person?

 

The numbers look accurate when the calculation is done for 3 minutes but when it is done for one minute, it looks fishy.

 

 

Accepted Answer

Ok, I get the 2nd part now. That's 6000 calls a month, with an average answer time per call of 1 min.

Well, if the time needed to answer a call is now only 1 min then it takes but 1/3 of the previous time, and that simply means that you only need 1/3 of the number of previous employees required.

The previous number was 2.174 employees. (rounded up to 3)
one third of that is 0.725 employees,
which accords pretty well with your own estimate.
So the answer to this part is.
Answer = 1 employee
================

================================================

Since you can't deal with fractions of a person (they wouldn't be able to work very well, would they!!), then you have to have a whole number, and that greater than the calculated (non-integer) value.

================================================

If you want a formula, then here it is.

Nc = number of calls/month
t = answer time per call (in mins)
D = days in month
M = months in year

Call answer time (over a year) to be covered by employees is T, where

T = NcMt
======

n = number of Employees
h = hrs worked per day

Annual coverage by employees is C, where

C = 60hnDM
========


We need C = T

60hnDM = NcMt
n = (Nct)/(60hd)
=============

Check
Form the first problem,

n = (6000*3)/(60*6*23) = 2.174 - OK

Edited by Fermat on 2/5/2009 at 11:40 PM

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Expert: Fermat
Pos. Feedback: 100.0 %
Accepts: 
Answered: 2/5/2009

Graduate Student

BSc Maths 1st class Hons; BSc Computer Science; HNC Mech. Eng.

Posted by Fermat 290 days and 9 hours ago.

Info Request

In that formula that I gave in my last post, you will have noticed that the number of months, M, gets cancelled out, and its value is never actually used, hence never needed.

I used that value when I was first working things out, simply because there was an unusual number of days in the month (23), so I thought I would have to work in annual terms. Now I can see that it's not needed, so you can amend that formula I gave to become,

60*h*n*D = Nc*t

and rearrange it to suit.

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