A company knows that unit cost C and unit revenue R from the production and sale of x units are related by C = ((R^2)/(182000)) + 8033 . Find the rate of change of revenue per unit when the cost per unit changing by $ 11 and the revenueis $ 4000.
A company knows that unit cost C and unit revenue R from the production and sale of x units are related by C = ((R^2)/(182000)) + 8033 . Find the rate of change of revenue per unit when the cost per unit changing by $ 11 and the revenueis $ 4000.
You want to find: $\displaystyle \frac{dR}{dx}$,
we start by differentiating $\displaystyle C$ with respect to $\displaystyle x$:
$\displaystyle \frac{dC}{dx} = \frac{d}{dx}\left[\frac{R^2}{182000} + 8033 \right]=\frac{R}{91000}\frac{dR}{dx}$
Now you want $\displaystyle \frac{dR}{dx}$ when $\displaystyle \frac{dC}{dx}=11$ and $\displaystyle R=4000$. Plug these into the above equation and solve for $\displaystyle \frac{dR}{dx}$.
RonL