Walls of a room with dimension 10 m × 10 m × 4 m need to be constructed using offsite prefabrication technique. Assuming the wall thickness 150 mm. The truck used for the transportation of the prefabricated components from the manufacturing unit to the construction site is of volume 15 m³ with the dimension of carriage 4 m (Length) × 3 m (width) × 3 m (height). Fix the dimension of the prefab wall components in a way that it takes minimum ___________ number of cycles by the loading truck for achieving the least transportation cost.

Concept:

To minimize the number of truck cycles for transporting prefabricated wall components, we need to consider the volume of the walls and the capacity of the truck.

Given Data:

• Room dimensions: 10 m (L) × 10 m (W) × 4 m (H)
• Wall thickness = 150 mm = 0.15 m
• Truck volume = 15 m³
• Truck dimensions: 4 m (Length) × 3 m (Width) × 3 m (Height)

Total Volume of Walls:

The surface area of the walls:

• Area of two longer walls: 2×(10×4) = 80m²
  $2 \times (10 \times 4) = 80 \, \text{m}^2$
• Area of two shorter walls: 2×(10×4) = 80 m²
  $2 \times (10 \times 4) = 80 \, \text{m}^2$
• Total surface area: 160m²
  $160 \, \text{m}^2$

Volume of walls = Surface area × Thickness of the walls:

\( \text{Volume of walls} = 160 \, \text{m}^2 \times 0.15 \, \text{m} = 24 \, \text{m}^3 \)

Prefabricated Wall Dimensions:

Assume the prefabricated wall panels are 4 m (Height) × 3 m (Width) × 0.15 m (Thickness), maximizing truck's space.

Volume of Each Prefab Component:

\( \text{Volume of each prefab panel} = 4 \times 3 \times 0.15 = 1.8 \, \text{m}^3 \)

Number of Panels per Truck Cycle:

\( \text{Number of panels per cycle} = \frac{15}{1.8} \approx 8 \, \text{panels} \)

Number of Panels Required:

\( \text{Number of panels required} = \frac{24}{1.8} \approx 14 \, \text{panels} \)

Number of Truck Cycles:

Given that the truck can carry 8 panels per cycle, the number of cycles needed is:

\( \text{Number of cycles} = \frac{14}{8} \approx 2 \, \text{cycles} \)

However, this calculation assumes that the truck is loaded to its full capacity. Since it's close to 14 panels, the final number of cycles needed will depend on the exact loading efficiency.

The number of truck cycles required is 14 cycles.