Question

An automated data processing pipeline evaluates five sequential stages ($k = 1, 2, 3, 4, 5$) to process machine learning workloads. At the start ($k = 0$), the system state is defined by Storage $S_0 = 10\text{ GB}$ and System Load $L_0 = 20\%$. At each subsequent stage $k$, the state vector $(S_k, L_k)$ updates according to the following rules:

- Stage 1 (Data Scrubbing): $S_1 = S_0 + 15$, $L_1 = L_0 + 10$
- Stage 2 (Feature Extraction): $S_2 = 2 \times S_1$, $L_2 = L_1 + 15$
- Stage 3 (Model Training): $S_3 = S_2 - 10$, $L_3 = L_2 + 25$
- Stage 4 (Batch Validation): $S_4 = S_3 + 20$, $L_4 = L_3 - 30$
- Stage 5 (System Deployment): $S_5 = S_4 - 25$, $L_5 = L_4 + 50$

The pipeline performance metric at any stage is defined as $M_k = S_k + L_k$.

Arrange the five stages in increasing order of their pipeline performance metric $M_k$ (from smallest value to largest value).