Question: How to SUM a variable number of VLOOKUP calls

Hello, I am trying to create a tool based in excel to be used by some data entry people in our company. I have two tables one that defines valid part names and their corresponding prices (sheet 1). And the other which is used to compose specific sale groups (sheet 2).

I would like to have the cost in sheet 2 determined by a sum of the prices of the parts in the row. I know I can use VLOOKUP to get the value of each part from sheet 1. However part of the goal is that both sheet 1 and sheet 2 will grow. So I want a formula for cost that takes into account that new parts and prices will be added to sheet 1 and that more parts can be added to sheet 2.

Any tips or help would be much appreciated.

Sheet 1 Sheet 2

Formatting got messed up.

Here is an example Excel File. View attachment Examle.xlsx

Array-Enter (using Ctrl+Shift+Enter, not just Enter on the keyboard) the following formula in cell B2:
=SUMPRODUCT(IF($C2:$E2=Prices!$A$2:$A$4,Prices!$B$2:$B$4,0))
then copy down.

Thanks, that worked great!