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Here is my take on the problem. My only problem is the newer version of Alteryx has a bug on the Find Nearest tool, I wasn't able to change the Maximum distance more than 100 miles even when I tried to type it in. However, I was able to work around it using the XML editor which I was able to change the max distance from 100 miles to 2000 miles.
To be honest, I got a little confused and had to check the solution to see what I was doing wrong.
When I read "distance for each item" I thought it was just the distance from each item id - store to the closest warehouse without multiplying the assigned amount of it.
Anyway, that's on me for not fully understanding the problem. I attached the correct solution and an extra tool to show what I was doing instead :)
Thank you.