There are a variety of ways of including price, but remember that for the customer price is not necessarily related to cost and what you're trying to do is understand how customers use price to indicate value.
The simplest method is to keep price as a single independent attribute and see how preferences vary by a price and feature combination - you can then evaluate the price value of individual items - in other words how preferences are counterbalanced by price. You may need to exclude the most extreme combinations.
If you want to infer prices for each individual attribute, then you will need to be more sophisticated. For instance, do you only allocate one value (or price delta value) to design/density/brand etc, or do you allow price to vary within design. If you fix the price are you already constraining what you think the customer values?
For instance it might be valid to have a low price high quality carpet from an unknown brand, compared to a high price, branded, but low quality carpet. If you make the assumption that high quality is high price for instance, you're already constraining the options. For this reason you may find it more useful to stick with a simple independent price variable.