11. If real numbers $x, y$ satisfy
$$
\left\{\begin{array}{l}
x-4 y+3 \leqslant 0, \\
3 x+5 y-25 \leqslant 0, \\
x \geqslant 1,
\end{array}\right.
$$

the maximum value of the objective function $z=k x+y$ is 12, and the minimum value is 3, then the value of the real number $k$ is ( ).
(A) 2
(B) -2
(C) $\frac{1}{5}$
(D) does not exist