Creating non-linear cost functions From what I understand, the basic cost function looks like
$$C(x_i)=\sum_{i=1}^{n}w_ix_i$$

What I'm wondering is whether or not its possible to create a non-linear cost function which adjusts based on the bundle consumed.

Example:

Lets say we have a discrete case where our  bundle price changes based on the combination of goods in a non-intuitive way. as seen in the table below.
$$\begin{array}{|c|c|c|c|}
\hline Bundle\ Price&amp;x_1&amp;x_2&amp;x_3
\\\hline 5&amp;1&amp;1&amp;0
\\\hline 10&amp;2&amp;1&amp;0
\\\hline 15&amp;2&amp;2&amp;0
\\\hline 25&amp;2&amp;3&amp;1
\\\hline
\end{array}$$

We see such pricing methods employed in a number of commercial businesses. 

How does one model such a case1?  



1. I would appreciate an answer that is more theoretical and does not rely upon regression , however if that is the only way to get an estimate i'll take it.
When you say non-linear cost function, I assume you aren't referring to the firm's production having non-linear costs, but judging by your example, you rather mean the firm's output prices having weird optimal bundle pricing.

From the abstract of the linked article (Hanson and Martin, 1990):


  " Bundle pricing is a widespread phenomenon. However, despite its importance as a pricing tool, surprisingly little is known about how to find optimal bundle prices. "


So this may be a good place for you to start. For an article that is a little more recent/available online, you could look at extensions of the original work in this area, such as bundle pricing for homogeneous items (Grigoriev et.al., no date), or this article correlated valuations for the items (Chen and Ni, 2017).