Saved Bookmarks
| 1. |
Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 - 24x - 6x2. |
|
Answer» Profit function is p(x) = 41 - 24x - 6x2 \(\therefore p'(x) = -24 - 12x\) & p''(x) = -12 < 0 \(\forall\) x \(\because\) p'(x) = 0 gives -24 - 12x = 0 ⇒ x = 24/-12 = -2 Hence, x = -2 is a critical point of function p(x) \(\because\) p''(x) = -12 ⇒ p"(-2) = -12 < 0 \(\therefore\) Critical point x = -2 is a point of maxima for profit function p(x). \(\therefore\) Maximum profit = p(-2) = 41 - 24 x -2 - 6 x (-2)2 = 41 + 48 - 24 = 41 + 24 = 65 Hence, maximum profit that company make is 65. |
|