A cylindrical container costs $2.00 per square foot for the sides and $3.00 a square foot for the top and bottom. The container must hold 100 cubic feet of material. What are the dimensions of the most economical container.

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Jan 4, 2007, 06:56 PM

ashley123456789
Precalculus - OPTIMIZATION

A cylindrical container costs $2.00 per square foot for the sides and $3.00 a square foot for the top and bottom. The container must hold 100 cubic feet of material. What are the dimensions of the most economical container.

Jan 5, 2007, 11:08 AM

galactus
The surface area of a cylinder(with top and bottom) is given by:

... [1]

Volume is: ... [2]

Remember your costs:

Using [1], the cost of the material would then be:

... [3]

Now, solve [2] for h and sub into [3]. You will then have the function in terms of r alone.

Differentiate, set to 0 and solve for r. Once you have r, h will follow.

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