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What mathematical model is needed to find the optimal solution in mathematical modeling?
Optimization method refers to the mathematical theory and method of seeking the reasonable allocation of limited resources and maximizing (or minimizing) one or more concerned indexes under a series of objective or subjective constraints, and is a very important branch of operational research.

Three elements: decision variables, decision variables, objective functions and constraints.

Feasible region: all x ranges that satisfy the constraint conditions.

Feasible solution: every solution in the feasible domain is called feasible solution.

Optimal solution: the solution that makes the objective function reach the optimal solution. It is divided into global optimal solution and local optimal solution.

Optimal value: the value of the objective function corresponding to the optimal solution.

Modeling background

Mathematical technology

Over the past half century, with the rapid development of computer technology, the application of mathematics has not only played an increasingly important role in engineering technology, natural science and other fields, but also penetrated into new fields such as economy, management, finance, biology, medicine, environment, geology, population and transportation with unprecedented breadth and depth. The so-called mathematical technology has become an important part of modern high technology.

Mathematical model is a kind of simulation, which is an abstract and concise description of the essential attributes of practical topics with mathematical symbols, mathematical formulas, programs and graphics. It can not only explain some objective phenomena, but also predict the future development law, and also provide an optimal strategy or a better strategy in a sense for controlling the development of a phenomenon.

Generally speaking, mathematical model is not a direct copy of real problems, and its establishment often requires people to observe and analyze real problems in depth and carefully, and also requires people to use all kinds of mathematical knowledge flexibly and skillfully. This process of abstracting mathematical models from practical problems with applied knowledge is called mathematical modeling.