Large language models (LLMs) have advanced natural language processing, but their massive parameter counts create computational and memory challenges during deployment. Post-training quantization (PTQ) has emerged as a promising approach to mitigate these challenges. While existing PTQ methods can effectively quantize LLMs, they experience substantial accuracy loss at extremely low bit-widths due to high-impact parameters. Several approaches address this by retaining high-impact parameters in FP16 format, but they apply fixed ratios across all layers, overlooking layer-wise sensitivity variations. We propose a quadratic optimization framework that determines layer-specific ratios of high-impact parameters while considering inter-layer dependencies. We quantize high-impact parameters to moderate bit-widths while the remaining parameters are quantized to extremely low bit-widths. Under the same resource budget, this preserves more high-impact parameters than methods retaining a few in FP16 format. Our framework enables leveraging advanced quantization methods for high-impact parameters while applying lightweight computational quantization methods to the rest, achieving an effective balance between computational efficiency and accuracy during quantization process.