Optimization problem

A cylindrical tin can is to be manufactured so that it will hold a specific volume V. If the materials for the ends of the can are twice as expensive as materials for the sides, what shape of can is most economical to manufacture? Find h in terms of r. Let the cost=$c per cm2, h is the height of the cylinder and r is the radius of the cylinder. You can assume that the cost is proportional to the surface area since the materials for a tin can have uniform thickness. Ignore the costs of forming the can, which are about the same for cans of any size 

answer is h=4r


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Erdos Erdos
  • Erdos Erdos

    Leave a comment if you need any clarifications.

  • Erdos Erdos

    Sorry, there was a small mistake. It is fixed now. Please double check and let me know if you have any questions.

  • Erdos Erdos

    Since the question is tagged as a calculus question, I used calculus techniques to solve it. This problem could also be solved using Lagrange Multipliers in multivariable calculus.

  • @James Oxenham: Please review the revised solution and let us know if you find it satisfactory.

The answer is accepted.
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