Funny to say, but once I've read this problem, I remembered
the simplex method we were taught last year.
The classic problem of simplex method is like this:
find min(max)f(X)=C1*X1+C2*x2+c3*x3.. where ci - constants
Also where is a system of conditions:
a11*x1+..<=(>=)b1
a21*x1+..<=(>=)b2 and so on.
The simplex method finds the solution very fast, but it can be a real value, not an integer. There is also a modification of SM called integer SM - it will find an integer solution. Is the problem based on this algo or not?

Thanks for allowing. I think I've seen in Kormen a chapter how to model linear programming with graphs (unbelievable, isn't it?). I'll see what will happen

I think you may round all BR down and all BC up to get integer solution.