Anyone interested in being paid to find a solution to a commercial problem?

We are software developers for the vacation rental business. We need
to code an availability search (in Microsoft SQL Server) to find the
cheapest combination of properties that will accommodate a given
capacity. Testing all possible combinations is not an option as forty
properties will yield roughly a trillion combinations. We have got to
the point where we take each property in turn, starting with the
cheapest in terms of cost per head, and then adding the next cheapest
and so on, until greater than or equal to the required capacity is
reached. If that capacity is reached EXACTLY, we then have a solution.
So far so good. But if we have gone over the required capacity, there
is a possibility that a different mix with a lower capacity will be
cheaper, even if the cost per head of capacity is higher, as a result
of the spare capacity in going over what is required rather than
matching it exactly.

We also need to be able to implement a solution WITHIN SQL Server as it
is extremely complex and difficult to call external software (we have
attempted unsuccessfully to do this with commercial linear programming
solutions).

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