In this paper, we explore a methodology for profitable and efficient optimization design of Multi-Service Internet backbone. The proposed method consists of two phases. In the first phase, a mathematical method based on a Linear Programming (LP) solution technique is utilized as primitive method with simplified objective functions and constraints. A Hopfield Neural Network (HNN) model is applied in the second phase to get an extended optimization for the network performance aiming to effectively distribute the network traffic across the network. The method has been developed and applied to the design of an Internet backbone network. Both models are formally defined, optimally formulated, and solved.