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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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    We use [this](http://en.wikipedia.org/wiki/Buckingham_Pi) in Fluid Mechanics.2012-02-21

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