Soru

A subscription service evaluates customer activity over a three-month period ($k = 1, 2, 3$). At the end of each month $k$, a customer's total loyalty points $P_k$ update based on their points from the previous month $P_{k-1}$ and the net points earned during month $k$ ($\Delta_k$), according to the state transition rule:

where $\lfloor x \rfloor$ represents the greatest integer less than or equal to $x$.

At the end of Month 3 ($k = 3$), membership tiers are assigned based on final points $P_3$:
- VIP Tier: $P_3 \ge 150$
- Premium Tier: $80 \le P_3 < 150$
- Standard Tier: $P_3 < 80$

Match each initial customer profile (defined by initial points $P_0$ and monthly additions $\Delta_1, \Delta_2, \Delta_3$) to its corresponding final state at the end of Month 3.