I knew going into this that we could only check so many combinations. Thats why I was searching only down to a configurable depth, probably only 3 to 5 deep. (A, AB, ABC, ABCD, etc) And unfortunately we need exact amounts. :( So we could have checks such as $100.30 and $20.75 to match for a search for $121.05.

I'm no mathematician, but I've certainly learned a lot from researching the knapsack problem. If anything it's given me some backing in telling the boss that there's only so much I can do to speed this up. :)