Mathematics > Vectors And Linear Programming > Linear Programming

The corner points of the feasible region of a Linear Programming Problem are $(0, 2)$, $(3, 0)$, $(6, 0)$, $(6, 8)$ and $(0, 5)$. If $Z=ax+by;$ ($a, b>0$) be the objective function, and maximum value of $Z$ is obtained at $(0, 2)$ and $(3, 0)$, then the relation between $a$ and $b$ is :