The maximum profit that a company can make if the profit function is given by
$P(x)=32+24x-18x^2$ is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 40
Profit function, $P(X)=32+24x-18x^2$
$⇒P'(x)=24-36x$
for critical points,
$24-36x=0$
$x=\frac{24}{36}=\frac{2}{3}$
and,
$P''(x)=-36$ which indicates that the function is concave down and at $x=\frac{2}{3}$ [maximum].
$∴P(\frac{2}{3})=32+24×\frac{2}{3}-18×\frac{4}{9}$
$=48-8=40$