Permutation List by Inventory and Value Total

Hello,
I am trying to create a list of permutations which select from an inventory of items, sometimes multiple or none based on an available quantity, and then check a reference value of those items to see if they meet a particular total. For instance, such a set:
(I apologize for the formatting of both of these tables. Whitespace I use while editing this post is being removed by the forum after submission.)

Item Quantity Value
Part A 0-2 100
Part B 0-4 70
Part C 0-4 40
Part D 0-6 10

By doing this manually I can create a permutation list that appears as this:
A B C D Total Pieces
1 0 2 3 4 300 9
2 0 2 4 0 300 6
3 0 3 1 5 300 9
4 0 3 2 1 300 6
5 0 4 0 2 300 6
6 1 0 4 4 300 9
7 1 1 2 5 300 9
8 1 1 3 1 300 6
9 1 2 0 6 300 9
10 1 2 1 2 300 6
11 2 0 1 6 300 9
12 2 0 2 2 300 6
13 2 1 0 3 300 6

I've done this manually using an inventory set up to approximately 80,000 rows, however now I have a larger inventory data set which results in approximately 1.4 billion rows, exceeding the limits of excel using my previous methods. I'm afraid I will have to purchase a C++ compiler to create a program which tests each permutation for the desired total value and then dumps entries to a text file, however I believe it is likely this can be done in Excel using methods I am not skilled enough to apply.

For example, I have attached the sample file I used to create this list. Sheet 1 is the raw data including every possible permutation. Sheet 2 contains the same data but sorted, with point per item subtotals hidden for formatting, and with a piece total. Sheet 3 is my desired final result, cut to show only those permutations which match the desired value total.

Thank you very much for taking the time to read my post! I hope you find this problem as intriguing as I do!

Hello again!
I have modified the code to use my new data set, however it is 2 hours into a run and has only calculated a fraction of the data. I attempted to replace some of the cell references with the actual values to reduce computation time but it doesn't seem to have reduced the number of minutes.

I also added some code to benchmark the speed of processing and output to the statusbar. I would never have attempted these things but seeing your code inspired me to try applying my own C++ knowledge. So far it's benchmarking at just over 2 days runtime! I hope after that I don't end up with over 1 million results, thereby exceeding the Excel limits again, and effectively making my document unprintable. Even so I'm beginning to believe the resulting list will be far too many pages for me to format for printing, negating some of the projects application.

I also added +1 to the pieces total to include a base starting piece, and also a check to limit number of total pieces to 48, not that those details are important to the code.

In any case, I wanted to share the resulting project document with you guys in case you have some wizardry that significantly reduces computation time!

Thank you very much again, this would have been literally impossible without your help!

(I figured out how to remove attachments after all so I've removed my previously uploaded v3 which contained errors.)

What are you going to do what all that data?