Find supremum of the function $f(x,y,z)=z^{4} (x^{2} - xy +y^{2}) + z^{2} (x^{4} + y^{4})$ on the tetrahedron, which veticies have coordinates (1,0,0), (0,2,0), (0,0,3) and (4,4,0).
Does anybody know if I have to check verticies, edges and faces separately, because it seems like it would create to many cases to consider.
