Help w/SUMPRODUCT with Three Arrays/Conditions/AND

I'm pretty sure that SUMPRODUCT is the solution to my problem here. I'm new to the SUMPRODUCT formula and fully understand it's basics and straight forward usage, however my SUMPRODUCT usage/requirement is a little more complex are I'm struggling with finding the right syntax to make things work for me.

I'm attempting to create a new data set that lists the FRAGMENTS (or components) needed for a given UPGRADE based on the ITEM (items are composed of fragments) requirements for an upgrade and the RECIPE of the FRAGMENTS to create an ITEM.

I have an insane spreadsheet to plug this into, but I've narrowed it down and simplified it to the attached spreadsheet. The whole vertical/horizontal array thing is screwing me up in my specific example.

Thanks for taking the time to have a peak at my challenge, I really appreciate it!

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