1. **Problem Statement:** Calculate the combined standard deviation of lead time and demand using the formula $$S_c = \sqrt{t \times S_d^2 + d^2 \times S_t^2}$$ where $S_t$ is the standard deviation of the replenishment cycle, $S_d$ is the standard deviation of demand, $t$ is the lead time, and $d$ is the average demand. 2. **Given Dummy Values:** - Lead time $t = 4$ days - Average demand $d = 50$ units/day - Standard deviation of demand $S_d = 8$ units - Standard deviation of replenishment cycle $S_t = 1.5$ days 3. **Step 1: Calculate each term inside the square root:** - Calculate $t \times S_d^2 = 4 \times 8^2 = 4 \times 64 = 256$ - Calculate $d^2 \times S_t^2 = 50^2 \times 1.5^2 = 2500 \times 2.25 = 5625$ 4. **Step 2: Sum the terms:** $$256 + 5625 = 5881$$ 5. **Step 3: Take the square root to find $S_c$:** $$S_c = \sqrt{5881} \approx 76.69$$ 6. **Interpretation:** The combined standard deviation of lead time and demand is approximately 76.69 units, which helps in determining safety stock levels to meet the desired service level. 7. **Service Level Note:** Choose a service level (e.g., 95%) to decide how much safety stock to keep, balancing inventory cost and stockout risk.