{
  "example_kind": "original synthetic manual planning case",
  "slug": "bounded-capacity-subset-selection",
  "title": "Select a feasible subset under a small capacity cap",
  "scenario": "Synthetic planning case: A toy portfolio has ten available hours and three independent, indivisible tasks. A needs six hours for twelve declared points; B and C each need five for nine.",
  "layout": "allocation",
  "dataset": {
    "heading": "Inspect the invented case records",
    "headers": [
      "Task or subset",
      "Hours",
      "Declared additive points",
      "Within cap?"
    ],
    "rows": [
      [
        "A",
        "6",
        "12",
        "Yes"
      ],
      [
        "B",
        "5",
        "9",
        "Yes"
      ],
      [
        "C",
        "5",
        "9",
        "Yes"
      ],
      [
        "B+C",
        "10",
        "18",
        "Yes"
      ],
      [
        "A+B or A+C",
        "11",
        "21",
        "No"
      ]
    ]
  },
  "derivation": "A ratio=12/6=2; B and C=9/5=1.8. Yet the feasible B+C bundle has eighteen points versus A’s twelve. The full three-task set needs sixteen hours and is infeasible.",
  "result": "B plus C fits ten hours and yields eighteen declared points. Choosing the highest single points-per-hour task A would yield twelve and leave four unusable hours in this case.",
  "boundary": "The guide tests a discrete bundle under a capacity cap and exposes a ratio-greedy failure.",
  "limitations": "Enumeration solves this small fully specified toy case only. Do not generalize it as a portfolio optimizer or ROI claim.",
  "sources": [
    "original"
  ],
  "tasks": [
    [
      "Confirm toy selection rules",
      "Decision owner",
      "Tasks are indivisible, independent and use additive declared points."
    ],
    [
      "Enumerate feasible subsets",
      "Planner",
      "B+C is feasible; both A pairings and the full set exceed capacity."
    ],
    [
      "Review the selected bundle",
      "Delivery lead",
      "The eighteen-point bundle is conditional on the stated rules and actual receiving criteria."
    ]
  ],
  "faqs": [
    [
      "Why not start A and part of B?",
      "This model treats tasks as indivisible outcomes; a valid split would change the model."
    ],
    [
      "Does a better point total prove a better real outcome?",
      "No. The points are declared preferences, not measured benefit, and missing constraints can change the choice."
    ]
  ],
  "method_references": [
    {
      "id": "original",
      "title": "Original worked-case definitions",
      "scope": "Definitions, policy choices, records and calculations are authored for this worksheet. No external standard, statistical validation or live product measurement is claimed."
    }
  ]
}