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 are 0.8 x 1.2 m and their maximum allowed load height is 1.3 m, but they are packed to the height of 1 m. When fully loaded with boxes, each pallet is 1.15 m high (this includes the height of the pallet itself). 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. Calculate the load factor on the pallet level (%).

To calculate the load factor on the pallet level, we need to determine how efficiently the pallets are being used in terms of volume.

1. **Volume of each box:**

   The inner dimensions of each box are:
   \[
   0.795 \, \text{m} \times 0.595 \, \text{m} \times 0.495 \, \text{m}
   \]

   So, the volume of each box is:
   \[
   0.795 \times 0.595 \times 0.495 = 0.234 \, \text{m}^3
   \]

2. **Number of boxes per pallet:**

   Each pallet is packed to a height of 1 meter, and each pallet's maximum loaded height including the pallet itself is 1.15 meters. The height of the pallet itself would then be:
   \[
   1.15 \, \text{m} - 1 \, \text{m} = 0.15 \, \text{m}
   \]

   The usable height for boxes on each pallet is 1 meter. Each box has an outer height of 0.5 meters. So, the number of boxes that can be stacked in height on each pallet is:
   \[
   \frac{1 \, \text{m}}{0.5 \, \text{m}} = 2
   \]

3. **Surface area of a pallet:**

   The dimensions of each pallet are:
   \[
   0.8 \, \text{m} \times 1.2 \, \text{m}
   \]

   The surface area of a pallet is:
   \[
   0.8 \times 1.2 = 0.96 \, \text{m}^2
   \]

4. **Box dimensions on the pallet:**

   The outer base dimensions of each box are:
   \[
   0.8 \, \text{m} \times 0.6 \, \text{m}
   \]

   The number of boxes that can be placed on one layer of the pallet (assuming perfect fit) is:
   \[
   \frac{1.2 \, \text{m}}{0.6 \, \text{m}} = 2 \quad \text{(along the length)}
   \]
   \[
   \frac{0.8 \, \text{m}}{0.8 \, \text{m}} = 1 \quad \text{(along the width)}
   \]

   So, the number of boxes on one layer is:
   \[
   2 \times 1 = 2
   \]

   Since each pallet can hold 2 layers of boxes:
   \[
   2 \times 2 = 4 \quad \text{(boxes per pallet)}
   \]

5. **Volume of boxes on each pallet:**

   The volume occupied by the boxes on each pallet is:
   \[
   4 \times 0.234 \, \text{m}^3 = 0.936 \, \text{m}^3
   \]

6. **Volume of the pallet space used:**

   The total volume of the space available on each pallet is:
   \[
   0.8 \, \text{m} \times 1.2 \, \text{m} \times 1 \, \text{m} = 0.96 \, \text{m}^3
   \]

7. **Load factor calculation:**

   The load factor is the percentage of the pallet volume that is occupied by the boxes. This is calculated as:
   \[
   \text{Load factor} = \left( \frac{0.936 \, \text{m}^3}{0.96 \, \text{m}^3} \right) \times 100\%
   \]

   Simplifying this:
   \[
   \text{Load factor} = \left( \frac{0.936}{0.96} \right) \times 100\% \approx 97.5\%
   \]

So, the load factor on the pallet level is approximately **97.5%**.

Do you want more details or have any questions? 

Here are 8 related questions for further exploration:

1. How is the load factor affected if the pallet height is increased?
2. What would be the new load factor if only 3 boxes are placed on each pallet?
3. How does the load factor change if the inner dimensions of the boxes are reduced?
4. What is the total weight capacity of the truck if each box weighs 2 kg?
5. How many pallets can fit into a truck with a given volume capacity of 44 m³?
6. What is the percentage of empty space in each box considering the volume of coat hangers?
7. How would the load factor change if the boxes were packed to 1.3 m height?
8. What is the efficiency of space utilization if 20 pallets are used instead of 24?

**Tip:** When calculating load factors, always consider both the volume and weight capacity limits to optimize transportation efficiency.

Learn how to calculate the load factor on the pallet level for transporting plastic coat hangers. This problem involves geometry, volume calculation, and percentage calculation, ensuring efficient packing and transportation logistics. Suitable for advanced high school students and beyond.

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