Max-Min Problem

[AK47]

I have a question:
What is the shape of a rectangular box with the largest possible volume for a given surface area if it has:

(a) all six sides?
(b) five sides but no top?

Full solutions would be GREATLY appreciated. Thanks.

 

[Deleted member 4993]

I have a question:
What is the shape of a rectangular box with the largest possible volume for a given surface area if it has:

(a) all six sides?
(b) five sides but no top?

Full solutions would be GREATLY appreciated. Thanks.

Please show us your work, indicating exactly where you are stuck, so that we know where to begin to help you.

To start draw a picture of the box, with,

Length = L

Width = W

Height = H

What is its volume?

What is its surface area?

Then continue....