1 Let $x \geqslant 0, y \geqslant 0, z \geqslant 0, x+y+z=1$, find the maximum and minimum values of $S=2 x^{2}+y+3 z^{2}$.
1. Fix the value of $z$, first find the maximum and minimum values of $2 x^{2}+y$, then let $z$ vary, find the overall maximum value $S_{\max }=3$, minimum value $S_{\min }=\frac{57}{72}$.