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3. A new company has asked you to design a new box for their product. You...

3. A new company has asked you to design a new box for their product. You and your design team are working on what to use and what sizes, given that the volume of the box must be 512 inches3.

a. Find a formula for the surface area of the closed, rectangular box, with a square base x inches by x inches and height h inches. Simplify your answer as much as possible. (I suggest drawing a picture!)

b. Find the dimensions giving the minimum amount of material (minimum surface area) of the closed rectangular box. You must use optimization methodology to solve this problem and you must show that this is a minimum. (Round your answer to 5 decimal places, if necessary).

c. What is the minimum surface area? (Round your answer to 3 decimal places, if necessary).

** please neatly show all steps using calculus and derivatives. If you can explain as well that would help**

Math   Calculus   
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