How to find the cost relationship with a few factors and a few numeric sizes?

I have a small data set (see attachment valve.txt or valve.csv), in which
there are a few facors: Type, ValveBody,Manufacturer
and a few numeric sizes: FlangeSize, Port.Size, Pressure and Cost.

I would like to find a statistics model that shows how Cost is related to
these factors and numeric sizes.
It seems to me that it is hard to find the relationship between Cost and a
few factors using regression models.

Could you please direct me on how to approach it? Thanks,

-james