The top and bottom of a can must be made of copper that costs two cents per square inch and the curved side is to be made of aluminum that costs one cent per square inch. Find the radius and height of the can that will maximize the volume of the can where the total cost of the can is 300pi cents.

Answer 1

Cost=.01*area of Al + .02*area of ends
300=.01*PI*radius*2*height+.01*PI*2*radius^2

Use that to find height as a functionof radius.

Now
Volume=PI*radius^2 * Height
set dVolume/drad =0 and solve for radius, then go back and solve for height.