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
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