I understand that the "bundle price" is cost to us. Then your table depicts a linear system of equations
$$C_j = a_1x_1+a_2x_2+...+a_mx_m,\;\;\; j=1,...,n$$
with $C_j$ and the $x$'s being the known quantities, and we want to determine the unknown alphas.
If it so happens that the bundles on offer are same in number as the $x$'s, ($n=m$), then the system, bar the existence of exact linear dependence, will ave a unique solution for the alphas, and the cost function will be linear.
But in your specific example, the system is "overidentified" ($n>m$) since you have more bundles on offer than inputs.
In such a case, "regression", or better, least-squares approximation enters the picture as a way to obtain a linear approximation, and also, quantify the deviation from actual through the obtained residual series.
In your example, one gets, $\hat a_1 = 3, \hat a_2=4, \hat a_3=7$, with estimated cost series $\hat C = 7,10,14,25$ compared to $C = 5,10,15,25$.
Essentially the estimated alphas here are the implied approximate separate unit prices per input, maintaining the linear relationship.
The non-linear approach would require to specify a non-linear function form first...and in principle, it would allow us to match the data exactly. The specified form could be found by trial and error, and it could be very complicated, which then would create the well-known issue: "well we matched the data sample exactly, but is this any good for inference/design outside the sample?"
In other words, assume we do obtain a non-linear cost function in such a way. Assume now that we want to produce at a level where we need to purchase $x_1 = 4, x_2=5, x_3=3$. Prior to go to the supplier and ask for a price for this new bundle, how well will the obtained non-linear cost function predict the offer we will get?