# RE8 | anthropic/claude-opus-5 | run 1

## Prompt

Minimize total time to finish these tasks, one at a time, respecting dependencies: A (2h, no deps); B (3h, needs A); C (1h, no deps); D (2h, needs B and C). Give a valid order and the total time.

## Response

**Total time: 8 hours** — since tasks run one at a time with no idle waiting, the makespan equals the sum of durations (2 + 3 + 1 + 2), and no ordering can beat that. The only thing order affects is *validity*, not speed.

## Valid Order

| Order | Task | Duration | Start → Finish |
|---|---|---|---|
| 1 | A | 2h | 0 → 2 |
| 2 | C | 1h | 2 → 3 |
| 3 | B | 3h | 3 → 6 |
| 4 | D | 2h | 6 → 8 |

**Sequence: A → C → B → D**

## Why It Works

A and C have no prerequisites, so either can go first. B requires A, which finishes at hour 2. D requires both B (done at hour 6) and C (done at hour 3), so D can start immediately at hour 6.

## Other Valid Sequences

- **C → A → B → D** (8h)
- **A → B → C → D** (8h)

Any order that places A before B, and both B and C before D, yields 8 hours. Invalid examples include B before A, or D before B.

*Note:* If parallel workers were allowed, the critical path A → B → D would set the floor at 7 hours, with C run alongside.

Would you like me to work out the optimal schedule for two or more parallel workers?
