consider the utility function u $2($x$)=$ x $1+2$x $2$ &if x $1+2$x $2<4,\backslash \backslash 4$& if $*4<=$ x$\_\{1\}+2$x$\_\{2\}<=8,\backslash \backslash$ x $1+2$x $2-4$&if x $1+2$x $2>8$ Determine the optimal demand for the two goods $($as a function of the relevant parameters$)$ Again, ensure that your mathemat$-$ ical arguments are technically sound.