With all do respect to our esteemed monk extremely is this not closer to the 'Knapsack' and 'bin packing' class of problems which can be solved using several non-brute force techniques therefore do not fall into the general class of NP-Complete problems.

There are several books that cover detailed solutions to these kinds of problems. My personal favourite is 'ALGORITHMS', Robert Sedgewick, Addison-Wesley, 1983.

Sedgewick describes some excellent approaches to your problem.

Computer Algorithms, Inroduction to Design and Analyssis, Sara Base, Addison-Wesley 1988 is also a good source.

mitd-Made in the Dark
'My favourite colour appears to be grey.'