# RE8 | google/gemini-3.6-flash | 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

To minimize total completion time when processing tasks sequentially on a single resource, all tasks must be executed without idle time in an order that satisfies all dependencies. Since the tasks are performed one at a time, the minimum total completion time is the sum of all individual task durations, which equals 8 hours. Valid execution orders include **A → B → C → D**, **A → C → B → D**, and **C → A → B → D**.

## Optimal Execution Schedule

Because tasks are processed sequentially, any topological sort of the dependency graph results in the same total duration of 8 hours.

| Task | Duration | Prerequisites | Start Time | End Time |
| :--- | :--- | :--- | :--- | :--- |
| **A** | 2 hours | None | 0:00 | 2:00 |
| **B** | 3 hours | A | 2:00 | 5:00 |
| **C** | 1 hour | None | 5:00 | 6:00 |
| **D** | 2 hours | B, C | 6:00 | 8:00 |

## Calculation and Verification

- **Total Duration:** \( 2\,\text{h} + 3\,\text{h} + 1\,\text{h} + 2\,\text{h} = 8\,\text{hours} \)
- **Dependency Checks:**
  - Task A starts immediately at 0h and finishes at 2h.
  - Task B requires Task A, so it starts at 2h and finishes at 5h.
  - Task C has no dependencies and finishes at 6h.
  - Task D requires both Task B (finished at 5h) and Task C (finished at 6h), so it starts at 6h and finishes at 8h.

Would you like to analyze how the completion time changes if you have multiple workers executing tasks in parallel?
