Question

Find the maximum profit that a company can make, if the profit function is given by $p(x) = 41 - 72x - 18x^2$

Answer 1

maximum value (m) is given by the y coordinate of the point of Maxima of this graph
$m = - \frac{d}{4a} \\ m = - \frac{ {b}^{2} - 4ac }{4a} \\ m = - \frac{ {72}^{2} - 4( 41)( - 18)}{4 \times ( - 18)} \\ m = - \frac{5184 + 2952}{ - 72} \\ m = \frac{8316}{72} \\ m = 113$
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