That's an interesting problem there. At the very least, you can say that the maximum might occur on an edge, and not just a corner. Just take the function Its maximum occurs on the edge
Now if a particulat constant is zero, then that whole corresponding product might as well not appear in the formula, right? So if we go on with that convention, you can restrict your constants to be in the set If you think about taking partial derivatives, one fact that might be important is that, since every variable appears in only a linear fashion in each product, when you take the partial derivative of the function with respect to that variable, that variable will not appear in its partial derivative. That implies that that variable's second partial derivative will be zero. I wonder if you could leverage that fact, since the maximum will occur (you have a continuous function there) either on a boundary of the domain, or at a critical point. The critical points are points where every partial derivative of the function is zero. So, if you could show that the critical points are all on the boundary of the domain, or outside the domain, you'd be done.
Those are the thoughts I have at present.