Historically, maximization problems have been a problem for calculus students. Not so much in finding critical points from functions and classifying them, but finding the objective function to begin with. Students rely on basic examples to mimic. We wonder why they can’t carry out more complicated examples. They are able to model simple physical situations after much practice, but flounder when faced with slightly more complicated problems because they don’t understand the complication well.

As the maximization and minimization problems become more complicated, using a table to organize examples of what is being modeled becomes more and more useful. Let’s look at another examples of how this might work.

**Problem** A rectangular tank with a square base, an open top, and a volume of 8788 ft^{3} is to be constructed of sheet metal. Find the dimensions of the tank that has the minimum surface area.