A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 567 cubic feet.  The conrete base costs $3 per square foot, the material for the roof costs $4 per square foot, and the material for the sides costs $4.50 per square foot.  Find the dimensions of the most economical shed.   Start out by finding the objective function with x representing the length of one of the sides of the base and C the cost of the shed.

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