Let the utility function $be$ given $byu(x_1,x_2)=\sqrt[\phantom{2}]{x_1}+\sqrt[\phantom{2}]{x_2}$ Let $mbe$ the income $of$ the consumer, $p_1$ and $p_2$ the prices $of$ good $1$ and good $2,$ respectively. $(a)$ Write down the budget constraint and illustrate the set $of$ feasible bundles using a figure.

$(b)Suppose$ that $m=24,p_1=2$ and $p_2=4.$ Find the optimal bundle for the consumer. $In$ other words, find the combination $of{x}_1$ and $x_2$that maximizes the consumer$s$ utility when the prices are $p_1=2$ and $p_2=4,$ and her income $ism=24.$

$(c)$ Determine the Marshallian demand function.

$(d)$ Determine the expenditure function.