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.