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. Then the minimum value of the objective function $z$ Occurs at

(0, 8)

The correct answer is Option (2) → (0, 8)

$z = 3x - 4y$

At $(0,0)$: $z = 3(0) - 4(0) = 0$

At $(5,0)$: $z = 3(5) - 4(0) = 15$

At $(6,5)$: $z = 3(6) - 4(5) = 18 - 20 = -2$

At $(6,8)$: $z = 3(6) - 4(8) = 18 - 32 = -14$

At $(4,10)$: $z = 3(4) - 4(10) = 12 - 40 = -28$

At $(0,8)$: $z = 3(0) - 4(8) = -32$

The minimum value occurs at $(0,8)$.