The solutions must lie in the quadrant . Negate these and add them together to get . Since p is 0 in the region of interest only at (0,0), this inequality tells us 0 is the maximum for p achieved at (0,0).
If you do use the simplex method,it suffices to check just the vertices. I think they are (0,0) (0,2) (2,3) (3,0).