MHB Minimizing Cost: Order Size for Optimal Price

[karush]

Minimum Cost The ordering and transportation cost $C$ of the components used in manufacturing a product is

$C=100\left(\frac{200}{x^2}+\frac{x}{x+30}\right),\ x\ge1$

Where $C$ is measured in thousands of dollars and $x$ is the order size in hundreds.
Find the order size that minimizes the cost. [Hint: use the roots feature of a graphing utility]

I took the derivative of this and set it to zero but did not get the ans of $4045$ units

from the graph it looks like the min would be 40.45 then times 100 would be the ans

thanks ahead

 

[MarkFL]

Re: minumum cost

Differentiating and equating to zero results in:

$\displaystyle 3x^3-40x^2-2400x-36000=0$

Using a numeric root-finding technique such as Newton's method yields the real root at:

$\displaystyle x\approx40.45$

Since x represents hundred of units, the answer is then 4045 units.

 

[karush]

Re: minumum cost

OK on the TI-Nspire Cas it was

zeros$\left(3x^3-40x^2-2400x-36000\right)\approx\ 40.45$