How to solve this : $R(m)=12+5m-0.4m^2$?
Jeremy's junkers keeps track of the revenue it makes from selling used exhaust manifolds. they have found that the revenue is a function of the number sold and this can be modeled by the quadratic function, where $R$ is the revenue in hundreds of dollars, and $m$ is the number of manifolds. How many manifolds should they sell to earn a revenue of $\$2400$?
The question asks us for the number, $m$, of manifolds sold when $R=24$ (since $R$ is measured in hundreds of dollars), thus we wish to solve this equation:
$$24=12+5m-.4m^2$$ $$\implies -\frac{2}{5}m^2+5m -12 =0$$ Using the quadratic forumula we obtain:
$$m =\frac{-5 \pm \sqrt{25-4(-2/5)(-12)}}{2(-2/5)}$$ $$= \frac{-5 \pm \frac{\sqrt{145}}{5}}{2(-2/5)}$$ $$=\frac{25 \pm \sqrt{145}}{4}$$
Thus we see that there are two quantities of manifolds, $ m \approx 3.24$ and $m \approx 9.26$ which will yield our desired revenue.
