Optimization Problem

[AustrianSaurkraut]

Please help! I am stuck on this question and any help will be appreciated.

Robert is designing a cylindrical garbage can. The open-topped can will have a volume of 24 000π cm3. The metal for the bottom of the can costs three times as much as the metal for the sides. Determine the ratio of the height to the radius for the dimensions of the can that will minimize the cost of the material.

 

[Deleted member 4993]

Please help! I am stuck on this question and any help will be appreciated.

Robert is designing a cylindrical garbage can. The open-topped can will have a volume of 24 000π cm3. The metal for the bottom of the can costs three times as much as the metal for the sides. Determine the ratio of the height to the radius for the dimensions of the can that will minimize the cost of the material.

Suppose the garbage can has a height of 'h' and radius of 'r'.

What is the volume of the cylindrical can?

What is the side surface area (surface area excluding the bottom) of the cylindrical can?

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