http://en.wikipedia.org/wiki/Knapsack_problem

There are entire books written about this subset of liner programming: subject

With unlimited supply, the greedy algorithm that takes the largest ratios first is guaranteed to reach $m/2$. With limited supply, it is far from optimal. TODO prove.

• http://www.amazon.com/Knapsack-problems-algorithms-computer-implementations/dp/B003KETJU0/

  Very readable.

• http://www.amazon.com/Knapsack-Problems-Hans-Kellerer/dp/3540402861/