Model Routing: Computing the Blended Savings

A ticket-triage system currently sends all 500,000 requests/day to a large model: 2,500 input tokens and 180 output tokens per request, at $1.00 per 1M input tokens and $3.00 per 1M output tokens. You train a lightweight classifier that safely routes 72% of requests to a small model priced at one-eighth of the large model's per-token rates, and sends the remaining 28% to the large model.

1. Compute the current daily cost (all traffic on the large model).
2. Compute the daily cost after routing is enabled, and the percentage reduction.
3. A colleague proposes a cascade instead: send 100% of traffic to the small model first, verify with a cheap judge call, and escalate 15% to the large model when the judge flags low confidence. What happens to latency for the 85% that don't escalate, and for the 15% that do, compared to the routing (classify-then-send) design in part 2?