# Mathematical model for my experiment?

I'm running a benchmark to find the efficiency of a my computer. There are $p$ control variables say, $x_1,x_2,...,x_p$ and one output variable $Y$. For example, every time I run an experiment I change the control variables and see the output (computer efficiency). So basically, for this problem I used regression to model this problem $\{Y_i,\, x_{i1}, \ldots, x_{ip}\}_{i=1}^n$. I used regression also because of the nature of the experiment i.e. If I'm conducting the same experiment in another computer I want to "fit" that computer w.r.t. to the values I have from my previous computer - which is fitting a line problem.

Now, in the new setting I have the same control variables but two outcomes $Y_{i1},Y_{i2}$ which are throughput and bandwidth. I'm trying to vary the control variables so as to maximize profit i.e. get $high$ throughput and consume $less$ bandwidth. How should I go about modeling this experiment?

I've knowledge of only basic linear algebra which is why I modelled first one using regression "easily". I would appreciate any help to put me thinking in the right direction.

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Coming from a Fluid Mechanics background, why not try dimensionless-like analysis on it? It could be interesting. It would be fairly empirical, at the end you might find something like $Y = x_1^{0.4545}\times x_2^{2.33} \cdots$ or whatever. Just a suggestion, may not even be useful. – Inquest Feb 21 '12 at 15:45
Very interesting. Could you give some more insights and some references as to where to look for it? – Sunil Feb 21 '12 at 16:12
We use this in Fluid Mechanics. – Inquest Feb 21 '12 at 16:15