• 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:

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

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

$6{\pi}r^{2}+4{\pi}rh$... [3]