The potential of mathematically sophisticated OR methods is currently not being fully utilized, as their application is limited to too few contexts and requires expertise. Our work explores the potential of using Generative AI (GenAI) to enable individuals lacking expertise in Linear Programming (LP) to utilize it with minimal training effort. We conducted a small laboratory study with management consultants of Deutsche Bahn. There we assessed their ability to solve optimization problems of various complexity using ChatGPT after only a short introduction into building optimization models. We introduced half of the participants to our framework for co-programming with GenAI. The results show that participants could successfully deploy LP solutions to straightforward problems, indicating a reduction in the entry barrier. GenAI therefore creates a potential for greater accessibility and interpretability, especially under guidance. However, the efficacy of GenAI support decreased as task complexity increased, increasing the risk of undetected incorrect solutions.