Question

Find the maximum profit that a company can make, if the profit function is given by p(x) = 41−24x−18x²

Answer 1

The profit function is given as p(x) = 41−24x−18x².

p'(x)=-24-36x

p''(x)=-36

Now,

p'(x)=0=x=-\(-\frac{24}{36}\)=\(-\frac{2}{3}\)

Also,

p'(\(-\frac{2}{3}\))=-36<0

By second derivative test,x=\(-\frac{2}{3}\) is the point of local maxima of p.

= Maximunm profit =p(\(-\frac{2}{3}\))

=41-24(\(-\frac{2}{3}\))-18(\(-\frac{2}{3}\))2

=41+16-8

=49

Hence, the maximum profit that the company can make is 49 units.