Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F = 4x + 6y be the objective function. The minimum value of F occurs at:

any point on the line segment joining the points (0, 2) and (3, 0)

The correct answer is Option (3) → any point on the line segment joining the points (0, 2) and (3, 0)

$F = 4x + 6y$

$F(0,2)=12$

$F(3,0)=12$

$F(6,0)=24,\;\; F(6,8)=72,\;\; F(0,5)=30$

$\text{Minimum value} = 12 \text{ at } (0,2) \text{ and } (3,0)$

$\text{Since objective function has same value at two vertices, it is constant along the line segment joining them}$

The minimum occurs at any point on the line segment joining $(0,2)$ and $(3,0)$.