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Sagot :
To compute the multifactor productivity (MFP) measure for each of the given weeks, we need to follow these steps for each week:
1. Calculate the weekly labor cost.
2. Calculate the overhead cost.
3. Calculate the material cost.
4. Add the labor cost, overhead cost, and material cost to get the total input cost.
5. Compute the multifactor productivity (MFP) by dividing the output by the total input cost.
Given data:
- Hourly wage = \[tex]$16 - Material cost per pound = \$[/tex]9
- Overhead is 1.5 times the weekly labor cost
For each week:
### Week 1
1. Weekly labor cost:
[tex]\[ \text{Labor Cost} = \text{Workers} \times \text{Hours per Week} \times \text{Hourly Wage} = 7 \times 40 \times 16 = 4480 \][/tex]
2. Overhead cost:
[tex]\[ \text{Overhead} = 1.5 \times \text{Labor Cost} = 1.5 \times 4480 = 6720 \][/tex]
3. Material cost:
[tex]\[ \text{Material Cost} = \text{Material (pounds)} \times \text{Cost per pound} = 410 \times 9 = 3690 \][/tex]
4. Total input cost:
[tex]\[ \text{Total Input Cost} = \text{Labor Cost} + \text{Overhead} + \text{Material Cost} = 4480 + 6720 + 3690 = 14890 \][/tex]
5. Multifactor productivity (MFP):
[tex]\[ \text{MFP} = \frac{\text{Output}}{\text{Total Input Cost}} = \frac{27000}{14890} \approx 1.81 \][/tex]
### Week 2
1. Weekly labor cost:
[tex]\[ \text{Labor Cost} = 8 \times 40 \times 16 = 5120 \][/tex]
2. Overhead cost:
[tex]\[ \text{Overhead} = 1.5 \times 5120 = 7680 \][/tex]
3. Material cost:
[tex]\[ \text{Material Cost} = 460 \times 9 = 4140 \][/tex]
4. Total input cost:
[tex]\[ \text{Total Input Cost} = 5120 + 7680 + 4140 = 16940 \][/tex]
5. Multifactor productivity (MFP):
[tex]\[ \text{MFP} = \frac{32000}{16940} \approx 1.89 \][/tex]
### Week 3
1. Weekly labor cost:
[tex]\[ \text{Labor Cost} = 8 \times 40 \times 16 = 5120 \][/tex]
2. Overhead cost:
[tex]\[ \text{Overhead} = 1.5 \times 5120 = 7680 \][/tex]
3. Material cost:
[tex]\[ \text{Material Cost} = 500 \times 9 = 4500 \][/tex]
4. Total input cost:
[tex]\[ \text{Total Input Cost} = 5120 + 7680 + 4500 = 17300 \][/tex]
5. Multifactor productivity (MFP):
[tex]\[ \text{MFP} = \frac{30000}{17300} \approx 1.73 \][/tex]
### Week 4
1. Weekly labor cost:
[tex]\[ \text{Labor Cost} = 7 \times 40 \times 16 = 4480 \][/tex]
2. Overhead cost:
[tex]\[ \text{Overhead} = 1.5 \times 4480 = 6720 \][/tex]
3. Material cost:
[tex]\[ \text{Material Cost} = 520 \times 9 = 4680 \][/tex]
4. Total input cost:
[tex]\[ \text{Total Input Cost} = 4480 + 6720 + 4680 = 15880 \][/tex]
5. Multifactor productivity (MFP):
[tex]\[ \text{MFP} = \frac{34000}{15880} \approx 2.14 \][/tex]
### Summary Table
\begin{tabular}{|c|c|}
\hline
Week & MFP \\
\hline
1 & 1.81 \\
2 & 1.89 \\
3 & 1.73 \\
4 & 2.14 \\
\hline
\end{tabular}
These calculations provide the multifactor productivity for each of the weeks.
1. Calculate the weekly labor cost.
2. Calculate the overhead cost.
3. Calculate the material cost.
4. Add the labor cost, overhead cost, and material cost to get the total input cost.
5. Compute the multifactor productivity (MFP) by dividing the output by the total input cost.
Given data:
- Hourly wage = \[tex]$16 - Material cost per pound = \$[/tex]9
- Overhead is 1.5 times the weekly labor cost
For each week:
### Week 1
1. Weekly labor cost:
[tex]\[ \text{Labor Cost} = \text{Workers} \times \text{Hours per Week} \times \text{Hourly Wage} = 7 \times 40 \times 16 = 4480 \][/tex]
2. Overhead cost:
[tex]\[ \text{Overhead} = 1.5 \times \text{Labor Cost} = 1.5 \times 4480 = 6720 \][/tex]
3. Material cost:
[tex]\[ \text{Material Cost} = \text{Material (pounds)} \times \text{Cost per pound} = 410 \times 9 = 3690 \][/tex]
4. Total input cost:
[tex]\[ \text{Total Input Cost} = \text{Labor Cost} + \text{Overhead} + \text{Material Cost} = 4480 + 6720 + 3690 = 14890 \][/tex]
5. Multifactor productivity (MFP):
[tex]\[ \text{MFP} = \frac{\text{Output}}{\text{Total Input Cost}} = \frac{27000}{14890} \approx 1.81 \][/tex]
### Week 2
1. Weekly labor cost:
[tex]\[ \text{Labor Cost} = 8 \times 40 \times 16 = 5120 \][/tex]
2. Overhead cost:
[tex]\[ \text{Overhead} = 1.5 \times 5120 = 7680 \][/tex]
3. Material cost:
[tex]\[ \text{Material Cost} = 460 \times 9 = 4140 \][/tex]
4. Total input cost:
[tex]\[ \text{Total Input Cost} = 5120 + 7680 + 4140 = 16940 \][/tex]
5. Multifactor productivity (MFP):
[tex]\[ \text{MFP} = \frac{32000}{16940} \approx 1.89 \][/tex]
### Week 3
1. Weekly labor cost:
[tex]\[ \text{Labor Cost} = 8 \times 40 \times 16 = 5120 \][/tex]
2. Overhead cost:
[tex]\[ \text{Overhead} = 1.5 \times 5120 = 7680 \][/tex]
3. Material cost:
[tex]\[ \text{Material Cost} = 500 \times 9 = 4500 \][/tex]
4. Total input cost:
[tex]\[ \text{Total Input Cost} = 5120 + 7680 + 4500 = 17300 \][/tex]
5. Multifactor productivity (MFP):
[tex]\[ \text{MFP} = \frac{30000}{17300} \approx 1.73 \][/tex]
### Week 4
1. Weekly labor cost:
[tex]\[ \text{Labor Cost} = 7 \times 40 \times 16 = 4480 \][/tex]
2. Overhead cost:
[tex]\[ \text{Overhead} = 1.5 \times 4480 = 6720 \][/tex]
3. Material cost:
[tex]\[ \text{Material Cost} = 520 \times 9 = 4680 \][/tex]
4. Total input cost:
[tex]\[ \text{Total Input Cost} = 4480 + 6720 + 4680 = 15880 \][/tex]
5. Multifactor productivity (MFP):
[tex]\[ \text{MFP} = \frac{34000}{15880} \approx 2.14 \][/tex]
### Summary Table
\begin{tabular}{|c|c|}
\hline
Week & MFP \\
\hline
1 & 1.81 \\
2 & 1.89 \\
3 & 1.73 \\
4 & 2.14 \\
\hline
\end{tabular}
These calculations provide the multifactor productivity for each of the weeks.
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