If the corner points of bounded feasible region for an LPP are (0, 2) (3, 0) (6, 0) (6, 8) and (0, 5) then the minimum value of the objective function $f=4x+6y$ occur at

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

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

Objective function: $f = 4x + 6y$

Corner points: $(0,2), (3,0), (6,0), (6,8), (0,5)$

Evaluate $f$ at each point:

$(0,2) \Rightarrow f = 4*0 + 6*2 = 12$

$(3,0) \Rightarrow f = 4*3 + 6*0 = 12$

$(6,0) \Rightarrow f = 4*6 + 6*0 = 24$

$(6,8) \Rightarrow f = 4*6 + 6*8 = 24 + 48 = 72$

$(0,5) \Rightarrow f = 4*0 + 6*5 = 30$

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

Since the objective function is linear, the minimum occurs at every point on the line segment joining $(0,2)$ and $(3,0)$

Answer: Every point on the line segment joining the points (0, 2) and (3, 0)