I’m having trouble with an optimization problem from MyOpenMath. My version of the problem looks like so:
A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.06 cents per square centimeter. Find the dimensions for the can that will minimize production cost.
I then need to find the radius, height, and minimum cost. Any suggestions?