# Select a feasible subset under a small capacity cap

Illustrative planning brief; no automatic product import.

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.

## Decision

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.

## Owned work

- Confirm toy selection rules
  - Owner role: Decision owner
  - Acceptance evidence: Tasks are indivisible, independent and use additive declared points.
- Enumerate feasible subsets
  - Owner role: Planner
  - Acceptance evidence: B+C is feasible; both A pairings and the full set exceed capacity.
- Review the selected bundle
  - Owner role: Delivery lead
  - Acceptance evidence: The eighteen-point bundle is conditional on the stated rules and actual receiving criteria.

## Workflow

1. Confirm toy selection rules. Check: Tasks are indivisible, independent and use additive declared points.
2. Enumerate feasible subsets. Check: B+C is feasible; both A pairings and the full set exceed capacity.
3. Review the selected bundle. Check: The eighteen-point bundle is conditional on the stated rules and actual receiving criteria.

## Judgment

Enumeration solves this small fully specified toy case only. Do not generalize it as a portfolio optimizer or ROI claim.


## Filled manual planning note

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. 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. Enumeration solves this small fully specified toy case only. Do not generalize it as a portfolio optimizer or ROI claim.


## Workflow questions

### 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.

## Product connection

Use the owned checks and downloaded brief to discuss this planning decision alongside your TeamBoostAI tasks. Confirm available fields, roles and account features separately. The example is manual; it does not calculate live analytics, create work or run an experiment in the product.

Confirm account availability before adopting this manual outline.

## Original worked case

Synthetic records, manual planning only. No account import or live analytics.

### Inspect the invented case records

Task or subset | Hours | Declared additive points | Within cap?
--- | --- | --- | ---
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

### Reasoning

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.

### Bounded 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.

### Distinct decision

The guide tests a discrete bundle under a capacity cap and exposes a ratio-greedy failure.

### Limits

Enumeration solves this small fully specified toy case only. Do not generalize it as a portfolio optimizer or ROI claim.

### Definitions and method context

- Original worked-case definitions — Definitions, policy choices, records and calculations are authored for this worksheet. No external standard, statistical validation or live product measurement is claimed.