A shipping company must design a closed rectangular shipping crate with a square base. The volume is $16524f{t}^3.$ The material for the top and sides costs $$3$ per square foot and the material for the bottom costs $$14$ per square foot. Find the dimensions of the crate that will minimize the total cost of material. Indicate the appropriate units in your answer.

In this exercise, you must verify that the critical number you find is a global maximum or minimum.