Thread: volume optimization

How do I go about doing this problem:

A box with a square base and open top must have a volume of 32000 cm3. Find the dimensions of the box that minimize the amount of material used.
1 cm (length and width)
2 cm (height)

Thanks!

Originally Posted by skeltonjoe

How do I go about doing this problem:

A box with a square base and open top must have a volume of 32000 cm3. Find the dimensions of the box that minimize the amount of material used.
1 cm (length and width)
2 cm (height)

Thanks!

Let s = the side of the base

Let h = the height of the box

The area of the base is

The area of the 4 sides is

You want to minimize

The volume must be 32000 so





Find the derivative of M, set it equal to 0 and solve for s. Then solve for h.