Question: A closed rectangular box with a square base and a volume of 12 cubic feet is to be constructed from two different types of materials.

A closed rectangular box with a square base and a volume of 12 cubic feet is to be constructed from two different types of materials. The top is made of a metal costing $2 per square foot and the remainder of wood costing $1 per square foot. Find the dimensions of the box for which the cost of materials is minimized.

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