Given inequations are

x, y ≥ 0, y ≤ 6, x + y ≤ 3

If we graph the inequalities y ≤ 6 and x + y ≤ 3 on the graph, we get the graph,

Here we can clearly see that, the region for the inequality is above the points A, B, C and D. But considering the constraints x , y ≥ 0, this clearly shows that the region can only be in the 1^st quadrant.

So from the green color highlighted area, we can say that, the region of the inequalities is unbound in the first quadrant.

Hence, the answer is option A.