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

F = 4x + 6y

Corner points - (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5).

Value of F at corner points –

At (0, 2), F = 12

At (3, 0), F = 12

At (6, 0), F = 24

At (6, 8), F = 72

At (0, 5), F = 30

Feasible region –

As, feasible region to be bounded so it is a closed polygon.

So, minimum value of F = 12 are at (3, 0) and (0, 2).

Therefore, minimum value of F occurs at, any point on the line segment joining the points (0, 2) and (3, 0).