ashley123456789 Posts: 2, Reputation: 1 New Member #1 Jan 4, 2007, 06:56 PM
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.
 galactus Posts: 2,271, Reputation: 282 Ultra Member #2 Jan 5, 2007, 11:08 AM
The surface area of a cylinder(with top and bottom) is given by:

$S=\underbrace{2{\pi}r^{2}}_{\text{top and\\bottom}}+\overbrace{2{\pi}rh}^{\text{cylinder }}$... [1]

Volume is: $V={\pi}r^{2}h=100$... [2]

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

$6{\pi}r^{2}+4{\pi}rh$... [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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