Context: Large Language Models (LLMs) are increasingly influencing software engineering practice and education. While prior studies examine their technical performance and classroom use, limited research provides cost-aware and empirically grounded models for systematic institutional integration. Objective: This study develops and validates a prediction model to identify cost-efficient strategies for integrating LLMs into software engineering education using motivating and demotivating factors. Method: Based on our previously developed literature survey taxonomies [1], we operationalized 19 validated factors (9 motivators and 10 demotivators) into a structured survey completed by 126 stakeholders from multiple countries. Likert-scale responses were encoded and used to train probabilistic models (Naive Bayes and Logistic Regression) to estimate the likelihood of high LLM familiarity. The probability estimates were integrated into a Genetic Algorithm (GA)-based optimization framework to model trade-offs between predicted familiarity and implementation cost at global and category levels. Results: Respondents perceived strong benefits in Programming Assistance and Debugging Support and Personalized and Adaptive Learning. Major concerns included Plagiarism and Intellectual Property Concerns, Over-Reliance on AI in Learning, and Reduced Critical Thinking and Problem Solving. Optimization results indicate that governance-related mechanisms, particularly integrity and ethical safeguards, should be prioritized under cost constraints. Conclusions: The study introduces an optimization-informed decision support framework linking stakeholder perceptions with probabilistic modeling and cost-effort analysis. The model supports staged and cost-aware LLM integration grounded in governance stability and pedagogically meaningful development.