1. **Problem Statement:** Calculate the overstock cost (Co), understock cost (Cu), critical ratio (CR), optimal cycle service level (CSL*), and optimal order quantity (Q*) for PT TrendMode selling winter jackets with given parameters. 2. **Given Data:** - Purchase cost $c=400000$ - Selling price $p=900000$ - Salvage value $s=300000$ - Demand $D \sim N(\mu=2000, \sigma=500)$ 3. **Step 1: Calculate Overstock Cost (Co) and Understock Cost (Cu)** - Overstock cost $Co = c - s = 400000 - 300000 = 100000$ - Understock cost $Cu = p - c = 900000 - 400000 = 500000$ 4. **Step 2: Calculate Critical Ratio (CR)** - Formula: $$CR = \frac{Cu}{Cu + Co}$$ - Substitute values: $$CR = \frac{500000}{500000 + 100000} = \frac{500000}{600000} = \frac{5}{6} \approx 0.8333$$ 5. **Step 3: Determine Optimal Cycle Service Level (CSL*)** - CSL* equals the critical ratio: $$CSL^* = CR = 0.8333$$ 6. **Step 4: Find the z-value corresponding to CSL* in the standard normal distribution** - From z-tables, $z_{0.8333} \approx 0.97$ 7. **Step 5: Calculate Optimal Order Quantity (Q*)** - Formula: $$Q^* = \mu + z \times \sigma$$ - Substitute values: $$Q^* = 2000 + 0.97 \times 500 = 2000 + 485 = 2485$$ 8. **Summary:** - Overstock cost $Co = 100000$ - Understock cost $Cu = 500000$ - Critical ratio $CR = 0.8333$ - Optimal cycle service level $CSL^* = 0.8333$ - Optimal order quantity $Q^* = 2485$ units 9. **Note:** For parts c) and d) of the original question, only part a) is solved here as per instructions.