$1.$ Suppose a consumer has a utility function such that U$=$ xy$/($x$+$y$)$ which is subject to a traditional budget constraint. Given this information, proceed to the questions below to solve the dual problem:

a$.$ Derive the uncompensated demand for x and y

b$.$ Derive the compensated demand for x and y

c$.$ Derive the indirect utility function

d$.$ Derive the expenditure function

e$.$ Derive the compensating variation $($CV$),$ equivalent variation $($EV$)$ and consumer surplus $($CS$).$ Assume income is $100($in thousands of dollars$)$ and that the price of good $\backslash ($ y $\backslash )$ increased from $\backslash (\backslash$$ $1\backslash )$ to $\backslash (\backslash$$ $3\backslash ).$ The price of good $\backslash ($ x $\backslash )$ is $\backslash (\backslash$$ $2\backslash )$ and does not change.