A firm has the following demand functions for each of its products and:

x $=720\mathrm{.}5$Px

y $=120-$ Py

The combined cost function is c $=$ x$2+$ xy $+$ y$2+35,$ and maximum joint production is $40.$ Calculate the profit maximizing level of:

$($i$)$ Output $(5$ Marks$)$

$($ii$)$ Price $(3$ Marks$)$

$($iii$)$ Profit $(2$ Marks$)$