Surface Area of Shoe Box Shape to Maximize Volume

[JuliusDarius]

Homework Statement

Imagine you have a rectangular piece of cardboard measuring 3 feet by 4 feet. You know that if you cut a square out of each corner, you can fold the pieces together and tape them together to make an object that looks like a shoe box:http://www.omahamathtutor.com/wp-content/uploads/2012/03/shoebox.png
What is the outside surface area of this shoe box shape that maximize the volume?

Homework Equations

2ab + 2bc + 2ac

The Attempt at a Solution

Not sure where to start

 

[Bohrok]

V = L*W*H

Then express the length, width, and height in terms of x after you remove those four squares from the 4 x [STRIKE]12[/STRIKE] 3 rectangle.

 

[JuliusDarius]

V = L*W*H

Then express the length, width, and height in terms of x after you remove those four squares from the 4x12 rectangle.

Could you show me how to do that?

 

[Bohrok]

The length is originally 4, then you cut off two segments of length x from both ends of that side, so L = 4 - 2x. Same thing for the width.

After cutting out the four squares, you have four flaps that fold up; what would be the height of these flaps?