The solution of problem about fermat point in application of the modern pipeline design

The transports of modern oil, gas and water are in need of pipeline design, usually we build on Extreme Value Model of polybasic function, and then find the numerical solution with mathematical software to make the pipeline construction costs to the minimum. This paper employs two basic situations between the pipeline design of the CPC pipeline and non-shared length pipeline with the same and different costs to establish the extreme model. And the classic problems and solutions of Fermat point are obtained to meet the analytical solution of the extreme value models.