3. Problem definition

The resource allocation problem can be formulated in two different ways:

1) Let X _i be the budget allocated for the i ^th project, and let f * _i be the performance associated with this resource allocation. We are looking for (X ₁ *, X ₂ *, X ₃ *, ..., X _n *) which maximizes the total profit from the overall allocation over the projects. This definition is consistent with the approach that seeks to maximize profit, given a given limited budget.

2) Let X _n be the budget allocated for...