Consider a $$rm with production function given by

f $($x$1$; x$2)=($x$1)1=4($x$2)1=2$ :

Assume the prices of inputs $1$ and $2$ are w$1$ and w$2,$ respectively, and the market price of

the product is p:

$($a$)$ Find the levels of the inputs that maximize the pro$$ts of the $$rm $($i$.$e$.,$ x

$1$ and x

$2).$

$($b$)$ Derive the supply function of the $$rm $($i$.$e$.,$ y $=$ f $($x

$1$; x

$2))$