The corner points of the bounded feasible region determined by the system of linear constraints are (0, 0), (5, 0), (6, 5), (6, 8), (4, 10), (0, 8). Let $Z = 3x - 4y$ be the objective function. The minimum value of Z occurs at

(0, 8)

The correct answer is Option (3) → (0, 8)

$Z = 3x - 4y$

$\text{Evaluate } Z \text{ at each corner point:}$

$Z(0, 0) = 3(0) - 4(0) = 0$

$Z(5, 0) = 3(5) - 4(0) = 15$

$Z(6, 5) = 3(6) - 4(5) = 18 - 20 = -2$

$Z(6, 8) = 3(6) - 4(8) = 18 - 32 = -14$

$Z(4, 10) = 3(4) - 4(10) = 12 - 40 = -28$

$Z(0, 8) = 3(0) - 4(8) = 0 - 32 = -32$

$\text{Minimum value of } Z = -32 \text{ at } (0, 8)$