What is the best way to find and print specific values by searching columns or locations in a certain order?

Edited to add: Picture of desired output.

I am trying to do this in Python but I also have access to SQL. I've included a simple example picture but the dataframes I'm working with are 1000s of items long. Basically I need to find a way to search dataframe

1. based on the the values in dataframe

2. I need to find the Qty Needed of each Item Number from dataframe 2 in Dataframe 1 but I have to search in a specific order.

If the entire quantity is in FR then stop and print each Item Number, Bin Location, and WH Code. If the entire quantity is not in FR then look at PV next then LH until the full quantity is reached.

output