A standard example of motivating constrained optimization are examples where the setup is described in a lot of lines, e.g., when you own a company and the company is making some products out of resources and are mixed in a certain ratio, etc.
Are there more easy (i.e., to explain and to understand) examples from daily life which motivate constrained optimization?
The examples should be nonlinear if possible, they don't have to be solvable, but it should be clear how to translate daily life language into the problem.
A great answer should also explain the need of constrained optimization tools (i.e., the constrains should not be solvable explicitly) and maybe also demonstrate that the gradient is not zero without calculating everything, but from the (first) view of the example.
Note: This question is related to Optimization problems that today's students might actually encounter?, where more advanced problems should be discussed.