Sizing and Justifying the Catalog Precompute Pipeline

Finance asks you to justify the catalog-mode rendering pipeline's infrastructure cost, and separately, a teammate proposes an alternative: skip precomputing catalog images entirely, and instead generate the "garment on a model" image live, on-demand, the first time any shopper views that product page (caching the result after that first view).

1. Using Step 1's catalog size and house-model-set assumptions, estimate the total number of renders the precompute pipeline needs to produce for the initial catalog, stating your assumptions explicitly.
2. Evaluate the teammate's "generate on first view, cache after" proposal. What does it get right, and what real risk does it introduce that the batch-precompute design avoids?
3. Is there a hybrid design that captures the teammate's intuition (don't waste compute on garments nobody views) without the risk you identified in part 2?