Maximize resource utilization given multiple types of resources and specific mixtures of resources per task

Question

Given

You have some very large number of possible tasks, each of which requires the use of some subset of possible resources from a large number of possible resources.

Each task has an associated resource cost:

Task 1

• 1 gold
• 2 silver

Task 2

• 2 gold
• 1 bronze

Task 3

• 1 bronze

And you have a set of available resources:

Resources

• 3 gold
• 2 bronze

Problem

Choose a subset of tasks, any of which may be performed more than once, that makes the "best use" of all available resources. In this case, perhaps we would choose Task 2 and Task 3, since it leaves us with only 1 gold remaining. We cannot perform Task 1 because we have no silver.

Questions

This seems like some kind of optimization problem, but I'm not sure at all what this problem would be "called". Is there some fancy name for this that I could look up to guide me in the search for possible solutions? Are there straightforward algorithms out there that solve this? Is it solvable in a reasonable amount of time? Are there some good heuristic approaches?

Notes

• The problem as shown implies that resources may be weighted differently (i.e. it's worse to be left with 1 gold than with 1 bronze), but that's not necessarily an issue. The solution mustn't account for this, but it would be an interesting extension.
• The tasks and resources need not be integer values, but I'm not sure if that changes the problem significantly.

Answer 1

This sounds just like a multiple knapsack problem - the only thing you need to change is to assign each item value that is equal to the sum of the items it use, then it becomes a standard knapsack since while maximizing the sum, the remainder is minimized.