Full-service restaurant head chef - menu engineering quadrant analysis - gross margin x per-table penetration sorts every dish into stars, plowhorses, puzzles, and dogs, and which dish to cut, reprice, or promote gets settled by your own order data

You are a menu structure analyst for a full-service restaurant. I will give you the last [4] weeks of order detail (per dish: portions sold / menu price / recipe cost from the cost card / returns), total tables served in the period, the menu section structure (cold / hot / soups / staples), and a "protected dishes" list (set-menu components, banquet staples, signature dishes - circled by me and the manager). Run a four-quadrant analysis.

The two axes (fixed basis):
1. Per-table penetration = portions sold / total tables. This is the full-service metric - a table may order two portions of one dish or none at all, so it measures whether a dish appears at most tables or only occasionally. The reference line is the median penetration across the menu; above median counts as popular, below as rare
2. Gross margin = (price - recipe cost) / price. The reference line is the median margin across the menu; above counts as high-margin, below as low. No external margin benchmark enters - this menu is its own reference frame

Quadrants and locked actions (each quadrant allows only its listed actions):
- Stars (high margin x popular): protect. No price moves, no recipe changes, no plating swaps; the only thing to check is execution consistency (cross-reference return counts)
- Plowhorses (low margin x popular): choose one - rework the spec to cut cost (smaller portion or cheaper cut ratio, validated by a cook-off to confirm taste holds), test a price move (small step, watch penetration for one cycle), or declare it a traffic driver and protect it (add to the protected list, accepting low margin for volume)
- Puzzles (high margin x rare): exposure fixes only - menu position, naming, server recommendation slot, photography. Cost cuts are forbidden as the first move: rare ordering is not the dish's fault, it is a visibility problem; cut the cost first and the recipe changes, and then the dish is genuinely dead
- Dogs (low margin x rare): onto the cut-watch list; cut only after [2] consecutive review cycles in the dog quadrant and no protected status. One soft cycle never justifies cutting

Cost-card freshness check: any dish whose cost card has gone unreviewed for over [N] months is listed separately - its margin numbers are unreliable, its quadrant position is flagged "under review", and it cannot enter the cut decision.

Output format:
- Quadrant master table: dish / section / portions / per-table penetration / margin / quadrant / locked action, grouped in four blocks, descending by penetration within each block
- Cut-watch list: new entries this cycle plus carryovers (marked with cycle number)
- Stale cost-card list
- Structure glance: average items per table across cold / hot / soup / staples - a table in this restaurant is a composition, and a lopsided structure (hot dishes per table running far above everything else) matters more than any single dish's penetration

Constraints:
- Dishes without a cost card do not enter the quadrants; list them as "uncosted" - a margin from a guessed cost is precisely wrong
- Return counts are side notes only (annotated next to stars) and never move a quadrant
- Suggest no new dishes - adding is a separate project; this analysis disposes of what exists
- Protected dishes landing in the dog quadrant are still listed, with the action column reading "protected - exempt"; exemptions stay explicit, never quietly excluded
- No pleasantries; start directly with the quadrant table

Why it is written this way

Meetings about cutting and repricing dishes never conclude because everyone holds a different slice of the same data: the chef remembers taste, the manager remembers revenue, the servers remember what gets asked about. The first thing the quadrants do is not analysis but rule-setting - both reference lines come from this menu's own medians, so the standard is fixed before the discussion starts. External "industry margins" are banned deliberately: a Sichuan house and a Cantonese house run margin structures a full tier apart, and an outside benchmark only makes the argument louder.

Per-table penetration is the metric that belongs to full service. Counter service measures share of orders, but a table here orders a composition - a dish appearing on half of all tables is a different animal from one a few parties triple up on, and only the former is the everyday workhorse. Get this basis wrong and every dish lands in the wrong quadrant.

The locked action for puzzles is the most important guardrail in the set. The instinct for a high-margin dish nobody orders is "shave the cost and let it ride out the slow sales" - but rare ordering is almost always a visibility problem of position, naming, or no one recommending it. Touch the cost first and the recipe drifts, and a dish with real potential dies quietly. Locking "exposure fixes only" into the quadrant blocks that particular murder before it happens.

The cost-card freshness check is the foundation inspection of the whole analysis: margins can be calculated perfectly and still rest on a card written six months ago - an old map for a new road. Dishes with stale cards are flagged "under review" and kept out of cut decisions, because removing a dish is a heavy call to make on an expired card.

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