The maximum value of the objective function Z = 3x + 5y, subject to the constraints: x + y ≥ 6; 3x + y ≥ 8; x ≤ 6; x, y ≥ 0 occurs at:

Not a finite point

The correct answer is Option (4) → Not a finite point

$Z=3x+5y$

$x+y \ge 6,\;\; 3x+y \ge 8,\;\; x \le 6,\;\; x,y \ge 0$

$\text{Feasible region is unbounded in } y \text{ direction}$

$\text{Since } y \text{ can increase indefinitely and } Z \text{ increases with } y$

$\Rightarrow Z \to \infty$

The maximum value is unbounded (infinite).