Your iron works has contracted to design and build a $\displaystyle 500ft^3$, square based, open top, rectangular steel holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weigh as little as possible.

These optimiziation problems are really getting to me, I have no idea where to start. Could anyone help solve it and/or provide tips on how I could get started. Thanks for the help.