Answer
$\mathrm{a}$.
$P(x)=-0.1x^{2}+23x-400$
$\mathrm{b}$.
$P(30)={{\$}} 200$
$\mathrm{c}$.
The profit on the sale of 30 clocks is ${{\$}} 200.$
Work Step by Step
$a$.
$P(x)=R(x)-C(x)$
$=30x-(0.1x^{2}+7x+400)$
$=30x-0.1x^{2}-7x-400$
$=-0.1x^{2}+23x-400$
$b$.
Substitute $x=30$ into the result of a.
$P(30)=-0.1(30)^{2}+23(30)-400$
$=-90+690-400$
$={{\$}} 200$
$c$.
When 30 clocks are sold, the profit is ${{\$}} 200.$
