Find the maximum and minimum values of $f$ and $g$ defined as $f(x,y) = 3x + 5y$ and $g(x,y) = 6x + 8y$ under the constraints: $2x - 3y \leq 6$, $2x + y \geq 2$, $2x + 3y \leq 12$, $x \geq 0$, $y \geq 0$.