MHB Maximizing Volume of a 5-Sided Box w/ Cutout Corners

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To maximize the volume of a five-sided box formed by cutting out corners from a sheet of dimensions L and W, the value of x must be determined. The surface area and volume equations are given as SA = 1LW + 2LH + 2WH and V = LWH, respectively. The problem involves optimizing the volume after the corners are removed and the flaps are folded up. A tutorial is suggested for further guidance on solving this type of maximizing problem. Understanding the relationship between the dimensions and the cutout size is crucial for achieving maximum volume.
Dustinsfl
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Consider a sheet of length L and width W.

Each corner is cut out (x by x corners removed).

Detemine the value of x so when the corners are removed and flaps folded up, the five sided box formed will have maximum volume.

SA \(= 1LW + 2 LH + 2WH\) and V \(= LWH\).

I am not sure how to do this maximizing problem.
 
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See http://mathhelpboards.com/math-notes-49/folding-make-boxes-6366.html for a tutorial on this kind of problem. :D
 

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