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This problem i need to use partial derivatives to solve but not Lagrange mulitpliers. My main problem is just setting it up:

A building in the shape of a rectangular box is to have a volume of 12,000 cubic feet. It is estimated that the annual heating and cooling costs will be $2 per square foot for the top,$4 per square for the front and back and $3 per square for the sides.(There is no cost for the bottom). Find the dimensions of the building that will result in a minimal annual heating and cooling cost. What is the minimum annual heating and cooling cost? Apply the second partial test to prove it is a minimum.

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# Minimization Problem

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