Creating an alphanumeric sequence using a column that determines the sequence

I keep track of an alphanumeric brand log at work that I'm currently calculating manually. Which at times is room for error. In one column is the number of tires that are ordered - in another column is the list of alphanumeric sequences that are branded on the tire. I've figured out a way I can do this if I want to list each brand in a cell, but that is not how this log is kept. Here is the example.

Brand# Qty Size
G21387-G21406 20 315/80R22.5
P21407-P21446 40 275/70R22.5
E21447-E21466 20 305/70R22.5

Each line has a different size tire so the brand starts with a different letter. The log is a range. Can this be calculated by putting the quantity (which is in column F in my spread sheet) and getting the results in Column A? How will I specify the leading alpha character in each row? Will it also depend on what column the tire size is in (which is in column G).

I've submitted an sample file - hopefully it will be helpful in determining a solution.

Thanks!