Question: A closed rectangular chest with a square base and a volume of 2000 cubic inches is to be constructed of two different types of materials.

A closed rectangular chest with a square base and a volume of 2000 cubic inches is to be constructed of two different types of materials. The top is made of metal costing $12 per square inch. And the remainder is made of wood costing $7 per square inch. Find the dimensions of the box for which the cost of the materials is minimized.

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