What would be the max volume one could make out of a sheet of metal?

For math, I have a 36 by 48 ft sheet of metal that i need to make a suitcase out of. I can cut off pieces to make a rectangular prism and need to find the maximum volume possible. Please explain to me the net, formula, and max volume u get. So far I have a volume of about 2600 and the formula is x(36-2x)(24-x).What would be the max volume one could make out of a sheet of metal?
Your working formula must be





V = x(36 - 2x)(48 - 2x)





and can be modified as





V = 1728x - 168x^2 + 4x^3





Differentiating,





dV/dx = 1728 - 336x + 12x^2





To get the maximum volume, set dV/dx = 0





dV/dx = 1728 - 336x + 12x^2 = 0





and solving for ';x'; (using the quadratic formula),





x = 6.78 feet





To have the maximum volume that can be fabricated, 6.78 feet must be cut off from the corner of the metal.





Hope this helps.What would be the max volume one could make out of a sheet of metal?
There are six sides to a cube. The formula is 1/6 times the area.

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