MHB What is the Optimal Production Level for Minimizing Average Cost per Unit?

[karush]

Average Cost. A manufacturer has determined that the total cost $C$ of operating a factory is
$C=0.5x^2+15x+5000$ where $x$ is the number of units produced.
At what level of production will the average cost per unit be minimized?
(The average cost per unit is $\frac{C}{x}$)

taking C' and setting to zero I got $-15$ but how is this going to give the ans which is
$x=100$ units.

thanks for help

 

[MarkFL]

You want to first compute:

$\displaystyle \frac{C}{x}=0.5x+15+5000x^{-1}$ where $\displaystyle 0<x$

Now, equate the derivative of this to zero.

 

[karush]

You want to first compute:

$\displaystyle \frac{C}{x}=0.5x+15+5000x^{-1}$ where $\displaystyle 0<x$

Now, equate the derivative of this to zero.

$(\frac{C}{x})'=\frac{1}{2}-\frac{5000}{x^2}$

$(\frac{C'}{x})'=0$ then x=100$ or $-100$ so $100$ is ans

r