Question

Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x².

पर्याय

• 25

• 43

• 62

• 49

Answer 1

49

Explanation:

The profit function is given as p(x) = 41 + 24x – 18x² 

∴ p'(x) = – 24 – 36x

p"(x) = – 36

Now, p'(x) = 0

⇒ x = `(-24)/36 = - 2/3`

Also, `p^('')((-2)/3) = - 36 < 0`

By second derivative test, x = `- 2/3` is the point of local maxima of p.

∴ Maximum profit = `p(- 2/3)`

= `41 - 24(- 2/3) - 18(- 2/3)^2`

= 41 + 6 – 8

= 49

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