The volume of a box is the amount of space in the box
The dimensions that minimize the cost of the box is 4 in by 4 in by 4 in
<h3>How to determine the dimensions that minimize the cost</h3>
The dimensions of the box are:
Width = x
Depth = y
So, the volume (V) is:

The volume is given as 64 cubic inches.
So, we have:

Make y the subject

The surface area of the box is calculated as:

The cost is:
--- the base is twice as expensive as the sides
Substitute 


Differentiate

Set to 0

Multiply through by x^2

Divide through by 4

Add 64 to both sides

Take the cube roots of both sides

Recall that:

So, we have:


Hence, the dimensions that minimize the cost of the box is 4 in by 4 in by 4 in
Read more about volume at:
brainly.com/question/1972490