Problems related to mathematical modeling, problems with mathematical modeling

with two-dimensional coordinates and the law of reflection.

The problems of mathematical modeling include the difficulty of modeling, the uncertainty of the model, the limitations of the data, and the applicability of the model to start and slow.

1. Difficult modeling:

Mathematical modeling relies heavily on the expertise and practical experience of the modeler, and the mathematical methods and tools used in modeling work are complex. Therefore, modeling for some special areas is very difficult and requires a high level of skill and expertise.

2. Uncertainty of the model:

Many real-world problems have high uncertainties, which makes it difficult for modelers to fully consider all factors when building models, resulting in errors. And the real world is changing very quickly, and the output of the mathematical model is likely to be the real situation in the future.

3. Limitations of data:

Mathematical modeling requires a large amount of data to support the construction and validation of models, but the cost of data acquisition is also high in practical problems, and the reliability of data is also limited. In addition, it is important to take care that the data collected is comprehensive, accurate, and reliable when modeling.

4. Applicability of the model:

The mathematical model established must be applicable to practical problems and provide reasonable solutions to practical problems. However, the applicability of the model is affected by real-world problems, so a lot of validation and tuning work is required for the model.

Modeling Applications:

Mathematics is the study of real-world quantitative relations and spatial forms, and it has been closely related to a variety of applied problems in the long history of its emergence and development.

The characteristics of mathematics lie not only in the abstraction of concepts, the rigor of logic, the clarity of conclusions and the integrity of the system, but also in the wide range of applications.

Since the 20th century, with the rapid development of scale science and technology and the increasing popularity of computers, people's requirements for various problems have become more and more precise, making the application of mathematics more and more extensive and deep, especially in the 21st century, the era of knowledge economy, the status of mathematical science will undergo great changes, it is moving from the reserve of the national economy and science and technology to the forefront.

With the globalization of economic development, the rapid development of computers, and the continuous expansion of mathematical theories and methods, mathematics has become an important part and think tank of contemporary high technology, and mathematics has become a technology that can be widely implemented.

Solution: (1) Modeling:

Set up the annual production of A type car A, B type car B, calculated according to the material: 2A + 2B = 1600 - A + B = 800 ....1)

Calculated by working hours: 5a+

Calculated by tire: a<=400....3)

2) Solve simultaneous equations (1) and (2) to obtain a and b values.

3) If a conforms to equation (3), i.e., if a<=400, then the values of a and b are taken as the planned scheme:Every year, a type A car is produced, and a type B car is taken. This is when the profit is maximum

4) If a>400, then let a=400, and substitute (1) and (2) respectively to obtain b1 and b2The smaller of A=400 and B1 and B2 is taken as the planned plan: 400 Type A cars will be produced every year, and Type B cars B1 or B2 (whichever is smaller of B1 and B2) will be produced. This is when the profit is maximum