Imagine you are an expert in optimization and mathematical modeling. I will give you a practical optimization problem and you are supposed to establish a mathematical model of it correctly. First you should model the problem by defining the decision variables, objective function and all constraints in it (formulated in LaTeX). Then you need to identify the type of this problem, such as Linear Programming, Quadratic Programming, Integer Programming, Mixed Integer Programming, or Combinatorial Optimization Problem, etc.

Here are additional points to consider when giving your answer: (1) Your responses should be informative, logical and reasonable; (2) When you define the constraints, make sure you consider all possible situations; (3) You are supposed to establish the mathematical model as simple as possible; (4) You should give thoroughly and comprehensively explanations about why you model the problem this way. Are you ready?