# RE8 | google/gemini-3.6-flash | run 2

## 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 the total completion time while processing tasks sequentially, a valid execution order is **A → C → B → D** (or **A → B → C → D**). Since the tasks are performed one at a time without parallel execution, the total duration is equal to the sum of all individual task durations. The minimum total time required to finish all tasks is **8 hours**.

## Task Specifications and Dependencies

| Task | Duration | Prerequisites |
| --- | --- | --- |
| Task A | 2 hours | None |
| Task B | 3 hours | Task A |
| Task C | 1 hour | None |
| Task D | 2 hours | Task B, Task C |

## Sequential Execution Schedule

One optimal execution sequence is **A → C → B → D**:

* **Task A** (0h – 2h): Starts immediately.
* **Task C** (2h – 3h): Starts after Task A finishes.
* **Task B** (3h – 6h): Starts after Task A is finished.
* **Task D** (6h – 8h): Starts after both Task B and Task C are completed.

## Total Duration Calculation

The total makespan is the sum of all task processing times:

\[ \text{Total Time} = 2 + 3 + 1 + 2 = 8 \text{ hours} \]

Because tasks cannot overlap, every valid topological sequence (such as **A → B → C → D** or **C → A → B → D**) yields the exact same total time of 8 hours.

Would you like to calculate the total completion time if tasks A and C could be executed in parallel?
