A closed cylindrical canister of 8pi cubic feet is to be made. It must stand between two partitions 8 feet apart in a room with a 8 ft. ceiling. If the cost of the top and bottom is $1 per square foot and the cost of the lateral surface of the cylinder is $2 per square foot, find the dimensions of the least expensive canister.
How would you draw a picture for this? And how would you solve this problem according to the min and max rates and such? Confused on where to start and how to get an answer?