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September 22, 2014

September 22, 2014

Posted by **Brian** on Wednesday, April 4, 2012 at 11:45pm.

- Math -
**Steve**, Thursday, April 5, 2012 at 11:15amwell, we know

4x+h = 96, so h=96-4x

v = hx^2

= x^2(96-4x)

= 96x^2 - 4x^3

= 4(24x^2 - x^3)

dv/dx = 4(48x - 3x^2)

= 12x(16 - x)

dv/dx = 0 when x = 0 or 16

so, h = 96-4*16 = 32

So, if the package is 16x16x32

v = 8192 in^3

Now, technically, 4x+h <= 96, but it should be clear that max volume occurs when 4x+h is as large as possible.

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