Discrete Optimization : Maximize profit while minimizing cost?

Data that I have :

Bids b (:,i) = [b1 b2 b3 ... bn]',
Cost c(:,i) = [C1 C2 C3 ... Cn]',
Revenue r(:,i) = [R1 R2 R3 ... Rn]'

I want to maximize sum of profit (Revenue - Cost) with a constraint on sum of Cost over all possible bids summed over i.

Result that I want : bid for each i and hence the cost and profit.

One approach was to do a regression and obtain polynomial fits for Cost and Revenue, but the data itself is very noisy and results in inflation of profit if the fit is not robust.

So instead of optimizing in continuous domain, I want to try discrete optimization. The way that I visualize it is there are a lot of small knapsack problems to be solved here. Any leads would be great!