Consider the utility function u $=2$

x $+4$y$.$

$($a$)$ Find ordinary $($Marshallian$)$ demand for the two goods as a function of income and prices.

$($b$)$ Find compensated $($Hicksian$)$ demand.

$($c$)$ Find the expenditure function and verify Shephard$$s Lemma.

$($d$)$ Find the indirect utility function and verify Roy$$s identity.