A square-based, box-shaped shipping crate with a volume of 16 cubic feet needs to be constructed at minimum cost. The material used for the sides of the box costs p dollars per square foot, while the material used for each square base (top and bottom of the crate) costs 2p dollars per square foot. What are the dimensions of the crate that minimize the cost of materials? Show all steps. Use appropriate units. Remember to use either the First Derivative Test or the Second Derivative Test to show that the cost has been minimized, and label the dimensions of the optimized shipping crate. Note: not to scale

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