{"id": "card_works_knapsack", "kind": "verified", "title": "The best a knapsack can carry", "body": "Given items of weight and value and a fixed capacity, the 0-1 knapsack picks the most valuable subset that fits — here a total value of 7 within a weight of 5. The core of scheduling, budgeting and cargo-loading.  Worked & sealed by the engine — 0-1 knapsack (cap 5) → optimal value 7.  [HOLDS; open the seal to re-check.]", "source": {"label": "The Works — worked & sealed", "url": "https://narrowhighway.com/s/146ec914dad0d44e177cd894b09742163848ac2508926d7b9d0a8d10b588c909", "domain": "operations_research", "authority_tier": "verified"}, "shelf": "the-works", "box": "engineering", "bands": ["the-works", "engineering", "operations_research", "operations", "research"], "connections": [{"to_card_id": "card_spine_the-works", "relationship": "member_of", "evidence": "a member of the the-works shelf in the keeping"}, {"to_card_id": "card_k_floor_of_discovery", "relationship": "paves", "evidence": "A worked, engine-sealed demonstration — a paving-stone of the floor of reality."}, {"to_card_id": "card_v_03794e9aea45", "relationship": "demonstrates", "evidence": "A worked demonstration in the same field (operations_research)."}, {"to_card_id": "card_works_exposure", "relationship": "adjacent", "evidence": "Neighbouring worked demonstrations in the same part of the volume."}, {"to_card_id": "card_works_spherical_tank", "relationship": "adjacent", "evidence": "Neighbouring worked demonstrations in the same part of the volume."}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "subject": "Operations research", "extra": {"seal_hash": "146ec914dad0d44e177cd894b09742163848ac2508926d7b9d0a8d10b588c909", "cite_url": "https://narrowhighway.com/s/146ec914dad0d44e177cd894b09742163848ac2508926d7b9d0a8d10b588c909", "demonstration_id": "works_knapsack", "verdict": "HOLDS"}, "presentation": {"glyph": "•", "kind_label": "engineering", "by": "The Works — worked & sealed", "authority": "verified", "posted": "", "standing": "", "link": {"url": "https://narrowhighway.com/s/146ec914dad0d44e177cd894b09742163848ac2508926d7b9d0a8d10b588c909", "host": "narrowhighway.com", "provider": "", "titled": "The best a knapsack can carry", "waybill_line": "", "reach": "", "embed": ""}}, "neighbors": [{"id": "card_spine_the-works", "title": "The Works — sealed, worked demonstrations", "relationship": "on the shelf of", "why": "a member of the the-works shelf in the keeping", "href": "/card/card_spine_the-works", "resolved": true}, {"id": "card_k_floor_of_discovery", "title": "The Floor of Discovery — one floor, and by its design the fear of God", "relationship": "paves", "why": "A worked, engine-sealed demonstration — a paving-stone of the floor of reality.", "href": "/card/card_k_floor_of_discovery", "resolved": true}, {"id": "card_v_03794e9aea45", "title": "0-1 knapsack (cap 5) → optimal value 7", "relationship": "demonstrates", "why": "A worked demonstration in the same field (operations_research).", "href": "/card/card_v_03794e9aea45", "resolved": true}, {"id": "card_works_exposure", "title": "The exposure value of a camera setting", "relationship": "adjacent", "why": "Neighbouring worked demonstrations in the same part of the volume.", "href": "/card/card_works_exposure", "resolved": true}, {"id": "card_works_spherical_tank", "title": "Sizing a spherical tank of radius 3", "relationship": "adjacent", "why": "Neighbouring worked demonstrations in the same part of the volume.", "href": "/card/card_works_spherical_tank", "resolved": true}]}