Quantifying a trade-off Let our data be a set of 2d points sampled from a line $ax+by=1$ (that we do not know) plus some noise $\nu$. 

This is meant to represent a frontier of development - we can build a car with a powerful engine or very fuel efficient, but it is hard to do both.

How can I go about estimating the line $ax + by = 1$?
Linear regression is easy.  Or you could build some self training AI NN and do it the hard way.

Engine vs fuel efficient trade off  would not be linear and there are so many other factors that go into a final trade off.  

You must trade off ALL factors to optimise the system.