13-26 Given $|y| \leqslant 1$, and $2 x+y=1$, then the minimum value of $2 x^{2}+16 x+3 y^{2}$ is
(A) $19 / 7$.
(B) 3 .
(C) $27 / 7$.
(D) 13 .
(China Shanxi Province Taiyuan City Junior High School Mathematics Competition, 1997)
[Solution] Given $-1 \leqslant y \leqslant 1$, and $2 x+y=1$, thus $0 \leqslant x \leqslant 1$.
Also, $2 x^{2}+16 x+3 y^{2}=2 x^{2}+16 x+3(1-2 x)^{2}$
$$
=14 x^{2}+4 x+3,
$$

we know that $z=14 x^{2}+4 x+3$ is a parabola opening upwards with the axis of symmetry at $x=-\frac{1}{7}$. In the interval $0 \leqslant x \leqslant 1$, its minimum value is 3. Therefore, the answer is $(B)$.