ChatGPT is an LLM that has recently emerged as a remarkable artificial intelligence language model. In this paper, we explore ChatGPT v3.5 and ChatGPT v4.0 capabilities and limitations in modeling and solving various types of network optimization problems, emphasizing energy efficiency. Particularly, we test solutions generated by ChatGPT v3.5 and ChatGPT v4 which is integrated with the Wolfram plugin, against solutions generated by the general-algebraic modeling system (GAMS). The results show that Chat-GPT v3.5 and v4 are capable of generating mathematical models for optimization problems while considering power-related metrics, such as energy consumption and cost. Moreover, ChatGPT can be used to generate mathematical models for large optimization problems and solve them.