Does the lid have to be made out of the same sheet of cardboard?
If not then you might be able to say that the Volume is x(30-2x)(40-2x) if you cut the corners of the sheet out as a square and make the box by folding up the edges.
Hi,
Currently doing a problem with max/min problems and Maximizing the volume.
A sheet of cardboard 30cm by 40cm is to be cut into a box with a lid. The box shape is one of a rectangular cereal box.
I have worked the total area to be:
120cm^2 = 2zy + 2xy + 2xz
But im now stuck on what to do?
I need to find the dimensions that will maximise the volume and prove that its a maximum.
The question is:
A sheet of cardboard 30cm by 40cm is to be cut into a box with a lid, as shown below.
Find the dimensions of the box that maximise the volume it contains.
Hint: remember to show that it is indeed a maximum.
The net is the same as this shape, however x,y,z are all different lengths.
http://spmath84109.blogspot.com/2010_02_01_archive.html