We need to solve the equations two at a time. Observe that

For the point (0, -2) if we insert this point into fourth inequality we see that

is not true. Also for the point (6, 0) if we insert this point into the first inequality we see that

is not true. Therefore the points (0, -2) and (6, 0) do not belong the constraint set. The corner points for the constraint set are (0, 3), (3, 0), (0, 0) and (30/7, 6/7). Now, to find the maximum value we need to substitute each corner point to the goal function. Observe that for the point (0, 0) we have

maximum point is 15 and the correct option is A.