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

The corner points of the feasible region are (0,2), (3,0), (6,0), (6,8), and (0,5).

The objective function is $F = 4x + 6y$.

In Linear Programming Problems, the minimum (or maximum) value of the objective function occurs at corner points of the feasible region.

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Evaluating $F$ at each corner point:

At $(0, 2)$:

$F = 4(0) + 6(2)$

$F = 0 + 12$

$F = 12$

At $(3, 0)$:

$F = 4(3) + 6(0)$

$F = 12 + 0$

$F = 12$

At $(6, 0)$:

$F = 4(6) + 6(0)$

$F = 24 + 0$

$F = 24$

At $(6, 8)$:

$F = 4(6) + 6(8)$

$F = 24 + 48$

$F = 72$

At $(0, 5)$:

$F = 4(0) + 6(5)$

$F = 0 + 30$

$F = 30$

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The minimum value is $F = 12$, which occurs at two points: $(0,2)$ and $(3,0)$.

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When the objective function has the same value at two adjacent corner points, that value occurs at every point on the line segment joining them.

The points $(0,2)$ and $(3,0)$ are adjacent corner points sharing a common edge of the feasible region.

The objective function $F = 4x + 6y$ represents a family of parallel lines. When two adjacent corners give the same value, the objective function line is parallel to that edge, meaning the entire edge has the same value.

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Therefore, the minimum value $F = 12$ occurs at every point on the line segment joining $(0,2)$ and $(3,0)$.