Given a polyhedron defined by a set of inequalities, I was asked to find a function that gets its maximum along one of the faces of the polyhedron. I calculated the normal to the face and said that was the function. Is it correct? Intuitively, it seems so to me. The follow-up question asked what function gets maximized along an intersection of two faces - I think it could be a linear combination of the normal vectors of those faces, but I'm not sure.
Any help would be appreciated.