I am trying to optimize an open cylinder with an elliptical base to get a maximum volume for a fixed surface area. However, I have no idea on how to proceed with this with volume alone (as I have no idea what the surface area should be)
Volume of cylinder with elliptical base: $(πR_1R_2)h$
Thanks, everybody!
The area is the height times the perimeter of the base, so you just want the end to have the maximum area for its perimeter. The circle is that curve, so you want a circular cylinder.