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Let x ft be the length of the base square and y ft be the height of the box.
The volume of the box is
Since the box has a volume of 15 cubic feet, then
You need to construct two squares from the metal that cost $3 per square foot.
The area of each square is and the total cost for these two squares is
The area of each side face is Then the total cost for sides is
Let S(x) be the function that represents total cost of the box, then
Find the derivative:
When then
The dimensions of the box are:
length and width -
height -