If the corner points of the feasible region for an LPP are (60, 0), (120, 0), (60, 30) and (40, 20), then the maximum value of the objective function Z = 5x + 10y occurs at:

every point on the line segment joining the points (120, 0) and (60, 30)

The correct answer is Option (4) → every point on the line segment joining the points (120, 0) and (60, 30)

$Z = 5x + 10y$

$Z(60,0) = 5(60) + 10(0) = 300$

$Z(120,0) = 5(120) + 10(0) = 600$

$Z(60,30) = 5(60) + 10(30) = 300 + 300 = 600$

$Z(40,20) = 5(40) + 10(20) = 200 + 200 = 400$

$\text{Maximum value } = 600 \text{ at } (120,0) \text{ and } (60,30)$

$\text{Hence, all points on the line segment joining these two points give same maximum}$

The maximum occurs at every point on the line segment joining $(120,0)$ and $(60,30)$.