Break-Even Pay-Per-Token API vs Dedicated GPU

MoE, Compression & Scaling DS practice problem on Onlearn.

Difficulty: medium.

Topics: Understanding Cost Efficiency in LLM Deployment: Pay-per-token vs Dedicated Infrastructure, Token-to-Cost Conversion Ratios, Amortized GPU Instance Costs, Multi-tenant API Pricing Models, Inference Throughput Benchmarking, Break-even Token Threshold Calculation, Cloud Economics, Computational Complexity, Infrastructure as a Service (IaaS), Capacity Planning, Operational Expenditure (OpEx), Tokenization Efficiency, GPU Utilization Rates, API Latency vs. Throughput, Fixed vs. Variable Cost Modeling, Scaling Elasticity.

Given a daily request volume, average tokens per request, the cost per million tokens (API), and the monthly fixed cost of a dedicated GPU instance, write a function that determines the break even point in terms of daily token volume and identifies whether it is more cost effective to use an API or a dedicated instance.