Let's solve both inventory management problems step by step as per the requirements. --- ## 1. Smartphone Inventory Management ### (a) Average Daily Demand **Formula:** \[ \text{Daily Demand} = \frac{\text{Annual demand}}{\text{Operating days per year}} \] **Given:** - Annual demand (\( D \)) = 15,000 units - Operating days per year = 360 days \[ \text{Daily Demand} = \frac{15,000}{360} = 41.67 \text{ units (rounded to two decimal places)} \] --- ### (b) Safety Stock (95% service level, \( z = 1.65 \)) **Formula:** \[ \text{Safety Stock} = z \times \sigma_d \times \sqrt{L} \] **Given:** - \( z = 1.65 \) - \( \sigma_d = 4 \) units - Lead time (\( L \)) = 10 days \[ \text{Safety Stock} = 1.65 \times 4 \times \sqrt{10} \] \[ \sqrt{10} \approx 3.16 \] \[ \text{Safety Stock} = 1.65 \times 4 \times 3.16 \approx 20.84 \] **Rounded to the nearest whole number:** \[ \boxed{21} \] --- ## 2. Jacket Inventory Management ### (a) Average Daily Demand **Given:** - Annual demand (\( D \)) = 8,000 units - Operating days per year = 360 days \[ \text{Daily Demand} = \frac{8,000}{360} = 22.22 \text{ units (rounded to two decimal places)} \] --- ### (b) Safety Stock (97.5% service level, \( z = 1.96 \)) **Formula:** \[ \text{Safety Stock} = z \times \sigma_d \times \sqrt{L} \] **Given:** - \( z = 1.96 \) - \( \sigma_d = 6 \) units - Lead time (\( L \)) = 15 days \[ \text{Safety Stock} = 1.96 \times 6 \times \sqrt{15} \] \[ \sqrt{15} \approx 3.87 \] \[ \text{Safety Stock} = 1.96 \times 6 \times 3.87 \approx 45.51 \] **Rounded to the nearest whole number:** \[ \boxed{46} \] --- ## **Final Answers** ### 1. Smartphone Inventory Management (a) **Average daily demand:** **41.67 units** (b) **Safety stock (95%):** **21 units** ### 2. Jacket Inventory Management (a) **Average daily demand:** **22.22 units** (b) **Safety stock (97.5%):** **46 units** --- **All calculations are shown clearly above. If you have any questions or need further breakdown, let me know!**