The corner points of the feasible region of a LPP with the constraints $x + 2y ≤ 40, 3x + y ≥ 30, 4x + 3y ≥ 60, x, y ≥ 0$ are

$(15, 0), (40,0), (4, 18), (6,12)$

The correct answer is Option (4) → $(15, 0), (40,0), (4, 18), (6,12)$

$\text{Constraints: }x+2y\le40,\;3x+y\ge30,\;4x+3y\ge60,\;x\ge0,\;y\ge0$

$L_1:x+2y=40,\;L_2:3x+y=30,\;L_3:4x+3y=60$

$L_1\cap L_2:(4,18)\;(\text{feasible})$

$L_2\cap L_3:(6,12)\;(\text{feasible})$

$L_1\cap L_3:(0,20)\;(\text{infeasible since }3x+y=20<30)$

$\text{With }y=0:\;3x\ge30,\;4x\ge60,\;x\le40\;\Rightarrow\;x\in[15,40]$

$\Rightarrow\;(15,0),\;(40,0)\;\text{feasible}$

${\text{Corner points }=\{(15,0),\;(40,0),\;(4,18),\;(6,12)\}}$