$\{$:$U=x^{}*y^{}$ where $+=1)$

$M=p_x*x+p_y*y$

$\{$:$[=x^{}*y^{}+(M-p_x*x*p_y*y)],[(A)\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}=x^{(-1)}*y^{}-p_x=0],[(B)\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{y}}=y^{(-1)}{x}^{}-p_y=0],[(c)\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}}=(M-p_x*x-p_y*y)=0]\}F.O.C$

$(c)\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}}=(M-p_x*x-p_y*y)=0$

Plogoing into $($c$)$

$M=p_x*x+p_y*y$

$M=\frac{}{}*p_y*y+p_y*y$

$M=p_y*y(\frac{}{}+1)$

$y^{**}=\frac{*M}{{}_x}$

$\frac{+}{}=\frac{1}{}$

$x^{**}=\frac{*M}{{}_x}$

oTTimal vALUES

FOR $x^{**}{y}^{**}$