Maximise $Z = x + y$ subject to $x + 4y \le 8,$ $2x + 3y \le 12,$ $3x + y \le 9$, $x \ge 0$ and $y \ge 0$.

Here, the given LPP is,

Maximise $Z = x + y$ subject to,

$x + 4y \le 8,$ $2x + 3y \le 12,$ $3x + y \le 9,$ $x \ge 0,$ $y \ge 0$.

On solving $x + 4y = 8$ and $3x + y = 9$,

we get
$x = \frac{{28}}{{11}},y = \frac{{15}}{{11}}$.

From the feasible region, it is clear that coordinates of corner points are

$(0,0),(3,0)$, $\left( {\frac{{28}}{{11}},\frac{{15}}{{11}}} \right)$ and $(0,2)$.

Hence, the maximum value is $3\frac{{10}}{{11}}$.