A container company wants to design an aluminum can that requires the least amount of aluminum...

  

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A container company wants to design an aluminum can that requires the least amount of aluminum but that contains exactly 16 fluid ounces (28.875 cubic inches). Find the radius and height of such a can. Solve by substitution and method of Lagrangian multipliers. Show all work and explain. (15 pts). Hint: Minimizing the amount of aluminum means minimizing the surface area of the can subject to the volume restriction. The surface area of the can is: A = 2πr² + 2πrh And cylinder volume is: V = mr2h A container company wants to design an aluminum can that requires the least amount of aluminum but that contains exactly 16 fluid ounces (28.875 cubic inches). Find the radius and height of such a can. Solve by substitution and method of Lagrangian multipliers. Show all work and explain. (15 pts). Hint: Minimizing the amount of aluminum means minimizing the surface area of the can subject to the volume restriction. The surface area of the can is: A = 2πr² + 2πrh And cylinder volume is: V = mr2h

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