A company manufactures plastic coat hangers that are packed in cardboard boxes for transportation. A shipment consists of 96 boxes where each box contains 150 coat hangers. Each box has the outer dimensions 0.8 x 0.6 x 0.5 m and the inner dimensions 0.795 x 0.595 x 0.495 m. The boxes are loaded on 24 pallets. The pallets  dimension is 0.8x1.2x1.15 m and the pallets are loaded on a truck. The available capacity in the truck is 44 m3. Each coat hanger has a volume of 0.000045 m3.
a.Calculate the load factor on the pallet level in percentage?

To calculate the load factor on the pallet level in percentage, we'll follow these steps:

### Step 1: Calculate the volume of a box.
- Outer dimensions of a box: \(0.8 \times 0.6 \times 0.5 \, \text{m} \)
- Volume of a box: 
  \[
  V_{\text{box}} = 0.8 \times 0.6 \times 0.5 = 0.24 \, \text{m}^3
  \]

### Step 2: Calculate the number of boxes per pallet.
- The number of pallets: 24
- The total number of boxes: 96
- Number of boxes per pallet:
  \[
  \text{Boxes per pallet} = \frac{96}{24} = 4 \, \text{boxes per pallet}
  \]

### Step 3: Calculate the total volume occupied by the boxes on a single pallet.
- Volume occupied by boxes on one pallet:
  \[
  V_{\text{boxes on pallet}} = 4 \times 0.24 = 0.96 \, \text{m}^3
  \]

### Step 4: Calculate the volume of a pallet.
- Pallet dimensions: \(0.8 \times 1.2 \times 1.15 \, \text{m} \)
- Volume of a pallet:
  \[
  V_{\text{pallet}} = 0.8 \times 1.2 \times 1.15 = 1.104 \, \text{m}^3
  \]

### Step 5: Calculate the load factor.
- Load factor on the pallet level:
  \[
  \text{Load factor} = \frac{\text{Volume occupied by boxes on pallet}}{\text{Volume of pallet}} \times 100
  \]
  \[
  \text{Load factor} = \frac{0.96}{1.104} \times 100 \approx 86.96\%
  \]

### Answer:
The load factor on the pallet level is approximately **86.96%**.

Would you like further details or have any additional questions?

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Here are 8 related questions:
1. What is the remaining unused volume on each pallet?
2. How many pallets can fit within the truck's available capacity?
3. What is the load factor for the entire truck?
4. How many additional boxes could be loaded if the pallet dimensions were larger?
5. How much volume does one coat hanger occupy in the box?
6. What is the total volume of all coat hangers in one box?
7. If the pallet height is reduced by 10%, how does that affect the load factor?
8. What would the load factor be if the number of boxes per pallet increased to 5?

**Tip:** When dealing with packing and transportation, understanding both load factors and material strength can lead to significant cost savings and efficiency improvements.

Learn how to calculate the load factor on the pallet level using dimensions of boxes, pallets, and truck capacity. This problem involves calculating volumes, understanding geometric packing, and applying load factor formulas. Suitable for advanced high school students and anyone interested in logistics and volume calculations.

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