1. The maximum value of the function $y=\sin ^{4} x \cdot \cos x+\sin x \cdot \cos ^{4} x$ $\left(0<x<\frac{\pi}{2}\right)$ is $\qquad$ .
$$
\begin{array}{l}
\text { II. 1. } \frac{\sqrt{2}}{4} . \\
y=\sin x \cos x\left(\sin ^{3} x+\cos ^{3} x\right) \\
=\sin x \cos x(1-\sin x \cos x)(\sin x+\cos x) . \\
\because \sin x \cos x(1-\sin x \cos x) \\
\quad \leqslant\left[\frac{\sin x \cos x+(1-\sin x \cos x)}{2}\right]^{2}=\frac{1}{4},
\end{array}
$$
$\therefore$ Therefore, the equality holds if and only if $\sin x \cos x=1-\sin x \cos x$, i.e., $x=\frac{\pi}{4}$.
Also, $\because \sin x+\cos x=\sqrt{2} \sin \left(x+\frac{\pi}{4}\right) \leqslant \sqrt{2}$,
$\therefore$ the equality holds if and only if $x=\frac{\pi}{4}$.
Hence, when $x=\frac{\pi}{4}$, $y_{\text {max }}=\frac{\sqrt{2}}{4}$.
$$