# Am I correct for this question?

#### bushra1175

##### Junior Member

My working out:

7,940/7 = around 1,134 hours of work that needs to be done

1,134/10 = 113 shifts to be done based on 10 hour work days

I've worked out that we need to prefer full time workers over part time workers as they have a higher output rate:

35/40 = 87.5%
17/20 = 85%

For full time workers, I need to increase the shifts by 12.5% to make up for the time they're not spending on calls

12.5% of 113 = 14 shifts, meaning full time workers need to work 127 shifts to get through 7,940 calls

Since full time workers work 5 days a week, I would divide 127 shitfs by 5, giving me 25 full time workers

since this was a timed test (2.5 mins per question), I don't have time to work out every combination so I estimate the 20 FT and 7 PT combo to be correct

#### blamocur

##### Full Member
In you solution what is the weekly number of calls that the workers can handle ?

#### bushra1175

##### Junior Member
A full time worker can handle 7*35 calls a week, which is 245
A part time worker can handle 7*17 calls a week, which is 119

If you use 15FT workers, you would need 36PT workers so option 1 is ruled out
If you use 20FT workers, you would need 25PT workers, so option 2 and 3 are ruled out
If you use 25FT workers, you would need 15PT workers, so option 4 is ruled out
If you use 28FT workers, you would need 9PT workers, so the correct answer would be 28FT and 10PT as this is the closest option. Thanks!

#### JeffM

##### Elite Member
There are two issues with this question. One is that we have no idea what you are studying so we do not know what kinds of math may apply. The other is that the problem requires a lot of assumptions to answer. For example, do part time workers get paid the same hourly wage as full time workers? For another, are there peak times?

On the assumptions of no wage differentials and no peak loads, you face 7940 calls. A full time worker can handle 7 * 35 = 245 calls per week. A part time worker can handle 17 * 7 = 119 calls per week. So we have

$f \ge 0,\ p \ge 0, \text { and } 245f + 119p = 7940.$
So yes you can just plug the numbers in and see what makes sense.

#### bushra1175

##### Junior Member
There are two issues with this question. One is that we have no idea what you are studying so we do not know what kinds of math may apply. The other is that the problem requires a lot of assumptions to answer. For example, do part time workers get paid the same hourly wage as full time workers? For another, are there peak times?

On the assumptions of no wage differentials and no peak loads, you face 7940 calls. A full time worker can handle 7 * 35 = 245 calls per week. A part time worker can handle 17 * 7 = 119 calls per week. So we have

$f \ge 0,\ p \ge 0, \text { and } 245f + 119p = 7940.$
So yes you can just plug the numbers in and see what makes sense.
Thanks Jeff. This question is actually part of a numerical practice test for job applications. There is no context