Maximum volume of an open box with a square base?
Mia Lopez 
A box with a square base and an open top is to be made. You have $1200\operatorname{cm}^2$ of material to make it. What is the maximum volume the box could have?
Here's what I did:
$$1200 = x^2+4xz;$$ where $x$ is length of base and $z$ is height of box.
Also, let the volume of box be $V$, then
$$V= x^2 z =x^2\left(\frac{1200-x^2}{4x}\right)=300x - (0.25)x^3$$
$$V ' = 300-\frac{3}{4}x^2$$
$$300=\frac{3}{4}x^2$$
$$x=20$$
so the max volume should be $300(20)-.25(20)^3 = 4000(\operatorname{cm}^3)$
I feel like this is incorrect but this is what I have tried. Thank you.
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