$4.$ Michael has the utility function U$($x$,$ y$)=$ x $+3$y$.$ a$.$ Michael$$s budget line if the price of x is $1$ and the price of y is $2$ and his income is $8.$ What bundle does Michael choose in this situation? $[[$ans: $(0,4).]]($a$)$ What bundle would Michael choose if the price of x is $1,$ the price of y is $4,$ and his income is $8?[[$ans: $(8,0).]]5.$ Assume that John consume only x and y and his utility is U$($x$,$ y$)=($x $!1)$a$($y $!2)1!$a$.$ If he has m dollars and faces px and py$,$ obtain his optimal consumption bundle. $[[[$ans: x $=$ a$($m $!$ px $!2$py$)/$px $+1$ and y $=(1!$ a$)($m $!$ px $!2$py$)/$px $+2.]]$