Functions And Modelling Exercises
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The hourly profit obtained from operating a fleet of \(n\) taxis is given by \(P\left( n \right) = -2{n^2} + 120n - 200.\) Find the maximum hourly profit.
\begin{align}
&P(n)=-2n^{2}+120 n-200 \text { is of the form } \\
&\text {of a parabola where } a=-2, b=120, c=-200\\
&\text {The axis of symmetry is } x=-\frac{b}{2a}\\
&\therefore x=\frac{-120}{2\times -2}=30\\
&\begin{aligned}
\therefore P(30)&=-2(30)^{2}+120 \times 30-200\\
&=\$ 1600/\mathrm{hr}
\end{aligned}
\end{align}
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