Study on optimal utilization model based on the Lagrangian function

The Lagrangian function was originally a classical form of mechanical equation, and now it has been widely used in various disciplines such as science, engineering, and economics. In this paper, we constructs the optimal utilization model of non-renewable resources by means of Lagrangian function based on the Hortling rule, and explains the model from practical application. On the basis of the above, this paper uses the optimal utilization model to analyze the resource utilization of coastline, and finally draws the following conclusions: Before the development of coastline resources, the local government should evaluate the quality of coastline resources, and then divide the level of them. A reasonable number of high-quality coastline can be exploited, while low-quality coastline can be protected as a strategic reserve resource. And the local government should compare the gains from the development of the coastline resources with the income of other types of investment projects. The government should decide whether to develop the coastline according to the results of the comparison, in order to achieve the maximum effectiveness of limited funds.