Using a few sentences, describe three optimization problems which can be encountered in engineering, business, or science. You may seek $($but cite$)$ existing research work, published in any scientific journal, for each of them. Classify the problems into numerical, combinatorial, discrete, and$/$or mixed integer programming.

You are designing an open$-$top cylindrical container with a minimum volume of $1m^3.$ Find the dimensions of the tank that will require as little material as possible. Redo the problem if the container is not open$-$