Optimise $Z=3x+9y$ subject to the constraints:

$x+3y ≤ 60, x + y ≥ 10, x ≤ y, x≥0, y ≥0$, then

Maximum value of Z occurs at all the points on the line segment joining (15, 15) and (0, 20).

The correct answer is Option (4) → Maximum value of Z occurs at all the points on the line segment joining (15, 15) and (0, 20).

$Z(15,15)=3×15+9×15=180$

$Z(0,20)=9×20=180$

∴ $Z_{max}$ occurs at all the point on the line segment joining $(15,15)$ and $(0,20)$.