Week one: Output is 392, number of workers is five, Material (foot) Is 2720. 

Week two: Output is 408, Number of workers and six, Material (foot) 2790. The weekly output A fabrication process is shown above, Together with a data for labor and material input. Standard selling price is $125 per unit. Overhead is charged weekly at the rate of $1500 plus 0.5 times direct labor cost. Assume a 40 hour work week and an hourly wage of $16.    Material cost is $10 per foot. What is the average multifactor productivity?

To calculate the average multifactor productivity (MFP), we need to consider all inputs—labor, material, and overhead—relative to the output.

### Steps to calculate the MFP:

1. **Labor Cost**:
   - Each worker works for 40 hours per week.
   - The hourly wage is $16.

   Therefore, the labor cost per week is:

   \[
   \text{Labor Cost} = \text{Number of Workers} \times 40 \times 16
   \]

2. **Material Cost**:
   - Material cost is $10 per foot.

   Therefore, the material cost per week is:

   \[
   \text{Material Cost} = \text{Material (foot)} \times 10
   \]

3. **Overhead**:
   Overhead cost is calculated as:

   \[
   \text{Overhead} = 1500 + 0.5 \times \text{Direct Labor Cost}
   \]

   where Direct Labor Cost = $\text{Number of Workers} \times 40 \times 16$.

4. **Total Input Costs**:
   The total input costs each week will be the sum of labor cost, material cost, and overhead.

   \[
   \text{Total Input Costs} = \text{Labor Cost} + \text{Material Cost} + \text{Overhead}
   \]

5. **Multifactor Productivity (MFP)**:
   The MFP is the ratio of total output to total input costs.

   \[
   \text{MFP} = \frac{\text{Output}}{\text{Total Input Costs}}
   \]

### Calculating for Week One:

- **Labor Cost for Week One**:
  \[
  \text{Labor Cost} = 5 \times 40 \times 16 = 3200
  \]

- **Material Cost for Week One**:
  \[
  \text{Material Cost} = 2720 \times 10 = 27200
  \]

- **Overhead for Week One**:
  \[
  \text{Overhead} = 1500 + 0.5 \times 3200 = 1500 + 1600 = 3100
  \]

- **Total Input Costs for Week One**:
  \[
  \text{Total Input Costs} = 3200 + 27200 + 3100 = 33500
  \]

- **MFP for Week One**:
  \[
  \text{MFP} = \frac{392}{33500} \approx 0.0117
  \]

### Calculating for Week Two:

- **Labor Cost for Week Two**:
  \[
  \text{Labor Cost} = 6 \times 40 \times 16 = 3840
  \]

- **Material Cost for Week Two**:
  \[
  \text{Material Cost} = 2790 \times 10 = 27900
  \]

- **Overhead for Week Two**:
  \[
  \text{Overhead} = 1500 + 0.5 \times 3840 = 1500 + 1920 = 3420
  \]

- **Total Input Costs for Week Two**:
  \[
  \text{Total Input Costs} = 3840 + 27900 + 3420 = 35160
  \]

- **MFP for Week Two**:
  \[
  \text{MFP} = \frac{408}{35160} \approx 0.0116
  \]

### Average Multifactor Productivity:

Finally, the **average multifactor productivity** across both weeks is the average of the MFP values from week one and week two:

\[
\text{Average MFP} = \frac{0.0117 + 0.0116}{2} \approx 0.01165
\]

Thus, the **average multifactor productivity** is approximately **0.01165**.

Would you like to explore more details or calculations?

### Related questions:
1. How is multifactor productivity different from single-factor productivity?
2. How do changes in material cost affect productivity?
3. What happens to productivity if the hourly wage increases?
4. How does overhead impact the total cost of production?
5. Can multifactor productivity be improved by optimizing labor or material usage?

**Tip**: Increasing output without proportionally increasing inputs can significantly improve multifactor productivity.

Week one: Output is 392, number of workers is five, Material (foot) Is 2720. Week two: Output is 408, Number of workers and six, Material (foot) 2790. The weekly output A fabrication process is shown above, Together with a data for labor and material input. Standard selling price is $125 per unit. Overhead is charged weekly at the rate of $1500 plus 0.5 times direct labor cost. Assume a 40 hour work week and an hourly wage of $16. Material cost is $10 per foot. What is the average multifactor productivity?

This problem involves calculating the average multifactor productivity for a fabrication process using data for labor, material, and overhead costs. Includes detailed steps for calculating labor cost, material cost, and total input costs for two weeks. Suitable for Grades 10-12.

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