ashley123456789
Jan 4, 2007, 06:56 PM
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
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]
Remember your costs:
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.