Question # $3$:

Consider an individual with preferences defined over two goods, $x,$ and $Y.$ This individual has preferences

that can be represented by the following utility function: $U(x,Y)=x^2+Y^2.$ Let $P_x=4$ and $P_y=8.$ In

addition, suppose this individual has an income of $$120.$ How much goods $x$ and $Y$ should the individual

buy to maximize utility?