This work presents an efficient methodology for fine-tuning large language models (LLMs) under resource constraints using QLoRA (Quantized Low-Rank Adaptation) on consumer-grade hardware. We demonstrate practical fine-tuning of Mistral 7B (7.24 billion parameters) on a 6GB VRAM GPU, achieving significant performance improvements for educational applications in classical literature. Our key contributions include: (1) Efficient 4-bit quantization with LoRA rank optimization, reducing memory footprint while maintaining model quality; (2) Novel application to Shakespearean text generation and literary analysis; (3) Comprehensive ablation studies demonstrating optimal configuration with rank 128; and (4) Practical framework for educational AI deployment under hardware constraints. We achieve successful fine-tuning in approximately 2 hours with 859 training steps, reaching a final loss of 0.33. The trained LoRA adapter requires only 249MB of storage, making it highly portable and accessible. Our approach demonstrates that advanced NLP capabilities can be developed on consumer hardware (RTX 3060 6GB), democratizing access to LLM fine-tuning for educational institutions and independent researchers. The methodology addresses critical challenges in parameter-efficient fine-tuning including quantization-aware training, gradient checkpointing, and optimal hyperparameter selection under memory constraints. Experimental results validate the effectiveness of QLoRA for specialized domain adaptation, with the fine-tuned model showing superior performance in Shakespearean text understanding and generation compared to the base model. The upload contains the complete thesis (21 pages), LaTeX source files, BibTeX bibliography with 24+ references, and 13 publication-quality figures at 300 DPI.