Give step-by-step solution with explanation and final answer:1. Smartphone Inventory Management A retailer manages inventory for a 2. Jacket Inventory Management A retailer manages inventory for a jac

Question

Give step-by-step solution with explanation and final answer:1. Smartphone Inventory Management A retailer manages inventory for a 2. Jacket Inventory Management A retailer manages inventory for a jacket
smartphone with the following data with the following data:
Parameter Symbol Value Parameter Symbol Value
‘Annual demand D 15,000 units ‘Annual demand D 8,000 units
Lead time L 10 days Lead time L 15 days
Operating days per year 360 days Operating days per year 360 days
Standard deviation of w units Standard deviation of o 6 units
daily demand daily demand
Formulas Formulas
+ Daily Demand = Annual demand + Operating days per year « Daily Demand = Annual demand + Operating days per year
+ Safety Stock = = x a, x vLead time, where = — 1.5 for a 95% service « Safety Stock = : x o, x vLead time, where : — 1.96 for a 97.5% service
level level
Tasks Tasks
(a) Calculate the average daily demand. Round to two decimal places. (@) Calculate the average daily demand. Round to two decimal places.
(b) Calculate the safety stock required for a 95% service level. Round to (b) Calculate the safety stock required for a 97.5% service level. Round to
the nearest whole number. the neare

VIPSolutions · Accepted Answer

Let's solve each of the inventory management problems step-by-step, as per the images.  
**I'll show calculations for each, and present the answers clearly as requested.**

---

### **1. Smartphone Inventory Management**

#### **(a) Average Daily Demand**
$$
\text{Daily Demand} = \frac{\text{Annual demand}}{\text{Operating days per year}} = \frac{15,000}{360} = 41.67 \text{ units (rounded to two decimals)}
$$

#### **(b) Safety Stock (95% service level, $ z = 1.65 $)**
$$
\text{Safety Stock} = z \times \sigma_d \times \sqrt{L} = 1.65 \times 4 \times \sqrt{10}
$$
$$
\sqrt{10} = 3.1623
$$
$$
1.65 \times 4 \times 3.1623 = 20.88
$$
$$
\text{Safety Stock} = 21 \text{ units (rounded to nearest whole number)}
$$

---

### **2. Jacket Inventory Management**

#### **(a) Average Daily Demand**
$$
\text{Daily Demand} = \frac{8,000}{360} = 22.22 \text{ units}
$$

#### **(b) Safety Stock (97.5% service level, $ z = 1.96 $)**
$$
\text{Safety Stock} = 1.96 \times 6 \times \sqrt{15}
$$
$$
\sqrt{15} = 3.87298
$$
$$
1.96 \times 6 \times 3.87298 = 45.54
$$
$$
\text{Safety Stock} = 46 \text{ units}
$$

---

### **3. Refrigerator Inventory Management**

#### **(a) Average Daily Demand**
$$
\text{Daily Demand} = \frac{12,000}{360} = 33.33 \text{ units}
$$

#### **(b) Safety Stock (90% service level, $ z = 1.28 $)**
$$
\text{Safety Stock} = 1.28 \times 3 \times \sqrt{8}
$$
$$
\sqrt{8} = 2.8284
$$
$$
1.28 \times 3 \times 2.8284 = 10.85
$$
$$
\text{Safety Stock} = 11 \text{ units}
$$

---

### **4. Car Battery Inventory Management**

#### **(a) Average Daily Demand**
$$
\text{Daily Demand} = \frac{10,000}{360} = 27.78 \text{ units}
$$

#### **(b) Safety Stock (95% service level, $ z = 1.65 $)**
$$
\text{Safety Stock} = 1.65 \times 5 \times \sqrt{12}
$$
$$
\sqrt{12} = 3.4641
$$
$$
1.65 \times 5 \times 3.4641 = 28.08
$$
$$
\text{Safety Stock} = 28 \text{ units}
$$

---

### **5. Board Game Inventory Management**

#### **(a) Average Daily Demand**
$$
\text{Daily Demand} = \frac{20,000}{360} = 55.56 \text{ units}
$$

#### **(b) Safety Stock (99% service level, $ z = 2.33 $)**
$$
\text{Safety Stock} = 2.33 \times 7 \times \sqrt{9}
$$
$$
\sqrt{9} = 3
$$
$$
2.33 \times 7 \times 3 = 48.93
$$
$$
\text{Safety Stock} = 49 \text{ units}
$$

---

### **6. Medical Kit Inventory Management**

#### **(a) Average Daily Demand**
$$
\text{Daily Demand} = \frac{6,000}{360} = 16.67 \text{ units}
$$

#### **(b) Safety Stock (97.5% service level, $ z = 1.96 $)**
$$
\text{Safety Stock} = 1.96 \times 4 \times \sqrt{14}
$$
$$
\sqrt{14} = 3.7417
$$
$$
1.96 \times 4 \times 3.7417 = 29.32
$$
$$
\text{Safety Stock} = 29 \text{ units}
$$

---

### **7. Table Inventory Management**

#### **(a) Average Daily Demand**
$$
\text{Daily Demand} = \frac{9,000}{360} = 25.00 \text{ units}
$$

#### **(b) Safety Stock (90% service level, $ z = 1.28 $)**
$$
\text{Safety Stock} = 1.28 \times 6 \times \sqrt{11}
$$
$$
\sqrt{11} = 3.3166
$$
$$
1.28 \times 6 \times 3.3166 = 25.47
$$
$$
\text{Safety Stock} = 25 \text{ units}
$$

---

### **8. Bicycle Inventory Management**

#### **(a) Average Daily Demand**
$$
\text{Daily Demand} = \frac{7,500}{360} = 20.83 \text{ units}
$$

#### **(b) Safety Stock (95% service level, $ z = 1.65 $)**
$$
\text{Safety Stock} = 1.65 \times 5 \times \sqrt{13}
$$
$$
\sqrt{13} = 3.6056
$$
$$
1.65 \times 5 \times 3.6056 = 29.71
$$
$$
\text{Safety Stock} = 30 \text{ units}
$$

---

### **9. Computer Mouse Inventory Management**

#### **(a) Average Daily Demand**
$$
\text{Daily Demand} = \frac{18,000}{360} = 50.00 \text{ units}
$$

#### **(b) Safety Stock (99% service level, $ z = 2.33 $)**
$$
\text{Safety Stock} = 2.33 \times 8 \times \sqrt{10}
$$
$$
\sqrt{10} = 3.1623
$$
$$
2.33 \times 8 \times 3.1623 = 58.96
$$
$$
\text{Safety Stock} = 59 \text{ units}
$$

---

### **10. Notebook Inventory Management**

#### **(a) Average Daily Demand**
$$
\text{Daily Demand} = \frac{14,000}{360} = 38.89 \text{ units}
$$

#### **(b) Safety Stock (97.5% service level, $ z = 1.96 $)**
$$
\text{Safety Stock} = 1.96 \times 7 \times \sqrt{16}
$$
$$
\sqrt{16} = 4
$$
$$
1.96 \times 7 \times 4 = 54.88
$$
$$
\text{Safety Stock} = 55 \text{ units}
$$

---

## **Summary Table**

| # | Product         | Daily Demand | Safety Stock |
|---|-----------------|-------------|-------------|
| 1 | Smartphone      | 41.67       | 21          |
| 2 | Jacket          | 22.22       | 46          |
| 3 | Refrigerator    | 33.33       | 11          |
| 4 | Car Battery     | 27.78       | 28          |
| 5 | Board Game      | 55.56       | 49          |
| 6 | Medical Kit     | 16.67       | 29          |
| 7 | Table           | 25.00       | 25          |
| 8 | Bicycle         | 20.83       | 30          |
| 9 | Computer Mouse  | 50.00       | 59          |
|10 | Notebook        | 38.89       | 55          |

If you need a detailed breakdown for any specific one, let me know!

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