13. Given $x>0, y \geqslant 0, x+2 y=\frac{1}{2}$, find the values of $x$ and $y$ for which $u=\log _{0.75}(8 x y+$ $\left.4 y^{2}+1\right)$ attains its maximum and minimum values, and determine these maximum and minimum values.
13. $x=\frac{1}{2}-2 y>0$, so $0 \leqslant y<\frac{1}{4} \cdot u=\log _{0.75}\left[-12\left(y-\frac{1}{6}\right)^{2}+\frac{4}{3}\right]$, when $y=\frac{1}{6}$, $x=\frac{1}{6}$, $u_{\text {min }}=-1$; when $y=0, x=\frac{1}{4}$, $u_{\text {max }}=0$.