A storage shed is to be built in the shape of a box with a square base ...

A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 810 cubic feet. The concrete for the base costs $4 per square​ foot, the material for the roof costs $6 per square​ foot, and the material for the sides costs $4.50 per square foot. Find the dimensions of the most economical shed.