Answer
a) Profit function $P(x) =-0.1x^2+23x-400$
b) $P(30) =\$200$
c) When $30$ clocks are sold, the profit is $\$200$.
Work Step by Step
a) We know we can find the profit function by subtracting the cost function from the revenue function.
$P(x) = R(x) -C(x)$
$=30x-(0.1x^2+7x+400)$
$=30x-0.1x^2-7x-400$
$=-0.1x^2+23x-400$
b) Given $x=30$, when substituted in profit function $P(x)$
$P(30) =-0.1(30)^2+23(30)-400$
$=-90+690-400$
$=\$200$
c) When $30$ clocks are sold, the profit is $\$200$
