how would you solve this particular optimization problem (which seems harmless):
A tank with a square base is more taller than it is wider. To build it, the sum of the perimeter of the base with the height must be more than $108 \ m$. What is the maximum volume of the tank?
I say that it is a hard problem because the constrain (the volume of the tank) is not really fixed. If it was, the base and the height would be the same ($36 \ m$) and the total volume $46656 \ m^3$.
What can be done in this case?
Please let me know if my translation was poor.