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A storage company must design a large rectangular container with a square base. The volume is...

A storage company must design a large rectangular container with a square base. The volume is 24576ft324576⁢ft3. The material for the top costs $12$⁢12 per square foot, the material for the sides costs $2$⁢2 per square foot, and the material for the bottom costs $12$⁢12 per square foot. Find the dimensions of the container that will minimize the total cost of material.

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