# Statistical model for my problem

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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Does it make sense to define $Z_{i}=Y_{i1}-Y_{i2}$ and to repeat your regression analysis? That makes a strong assumption about the tradeoff between throughput and the cost of bandwith, which is that they can be compared one for one. That may be like comparing oranges and orangutangs and I don't know enought about your problem to tell. A more sophisticated approach would be to convert both throughput and the bandwith into dollars (or another currency, or just a common scale), with $Z_{i}=Benefit(Y_{i1})-Cost(Y_{i2})$.