Revenue A small business assumes that the demand function for one of its new products can be modeled by $p=C{e}^{kx}.$

When $p=$$$40,x=900$ units, and when $p=$$$30,x=1500$ units.

$($a$)$ Solve for $C$ and $k.($Round $C$ to four decimal places and $k$ to seven decimal places.$)$

$c=$

$k=$

$($b$)$ Find the values of $x$ and $p$ that will maximize the revenue for this product. $($Round $x$ to the nearest integer and $p$ to two decimal places.$)$

$x=$ units

$p=$$