I was speaking to a friend and they explained that the problem is my objective function.

That now leaves me with a whole new problem - what is my objective function.

I'm going to give the full brief, in order to make it easier to understand.

Work in a call centre, carrying out surveys with the general public.
We have quotas to achieve - in this case the quotas are as follows:

Male >=441
Female >=459

18-29 >=147
30-44 >=297
45-59 >=243
60-74 >=171

AB >=207
C1C2 >=396
DE >=231

Total >=1000

The quotas interlock, i.e. you can have a Male 45-59 DE or equally Female 19-29 C1C2.

As it transpires, my objective is to minimise the productive time.

Productive time = find time + interviewing time

The interviewing time currently stands at 7.65 minutes per person that we would speak with.

It is currently taking about 12.92 minutes to find someone to take part. The proportions in which they agree are as below.

Male 18-29 AB = 1.78%
Male 30-44 AB = 2.03%
Male 45-59 AB = 4.82%
Male 60-74 AB = 4.57%
Male 18-29 C1C2 = 8.63%
Male 30-44 C1C2 = 3.55%
Male 45-59 C1C2 = 6.85%
Male 60-74 C1C2 = 5.58%
Male 18-29 DE = 4.06%
Male 30-44 DE = 1.27%
Male 45-59 DE = 2.03%
Male 60-74 DE = 3.05%
Female 18-29 AB = 2.03%
Female 30-44 AB = 3.05%
Female 45-59 AB = 4.57%
Female 60-74 AB = 2.03%
Female 18-29 C1C2 = 7.11%
Female 30-44 C1C2 = 5.08%
Female 45-59 C1C2 = 8.88%
Female 60-74 C1C2 = 7.61%
Female 18-29 DE = 1.78%
Female 30-44 DE = 1.52%
Female 45-59 DE = 4.06%
Female 60-74 DE = 4.06%

The targets that I set for these interlocked quotas (Male 18-29 AB etc) must result in satisfying the constraints given above (Male >=441 etc).

Once I hit the target for a given quota, I do not interview them, thus the interviewing time = 0 on that instance (would have been 7.65 minutes), however, the find time still naturally increases.

So, the question is, what should I set the targets to in order to minimise the productive hours.

Thanks,