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Sagot :
To calculate the multifactor productivity (MFP) for each week, we'll follow these steps:
1. Calculate the total labor cost.
2. Calculate the overhead cost.
3. Calculate the material cost.
4. Sum the total input costs (labor, overhead, and material costs).
5. Compute the MFP by dividing the output by the total input costs.
6. Round the MFP values to two decimal places.
### Week 1:
Given:
- Output: 31,000 units
- Workers: 4
- Material: 460 pounds
Steps:
1. Labor Cost:
[tex]\[ \text{Labor Cost} = \text{Workers} \times \text{Hours per Week} \times \text{Hourly Wage} = 4 \times 40 \times 16 = 2560 \text{ dollars} \][/tex]
2. Overhead Cost:
[tex]\[ \text{Overhead Cost} = 1.5 \times \text{Labor Cost} = 1.5 \times 2560 = 3840 \text{ dollars} \][/tex]
3. Material Cost:
[tex]\[ \text{Material Cost} = \text{Material} \times \text{Material Cost per Pound} = 460 \times 9 = 4140 \text{ dollars} \][/tex]
4. Total Input Costs:
[tex]\[ \text{Total Input Costs} = \text{Labor Cost} + \text{Overhead Cost} + \text{Material Cost} = 2560 + 3840 + 4140 = 10540 \text{ dollars} \][/tex]
5. MFP:
[tex]\[ \text{MFP} = \frac{\text{Output}}{\text{Total Input Costs}} = \frac{31000}{10540} \approx 2.94 \][/tex]
### Week 2:
Given:
- Output: 36,000 units
- Workers: 5
- Material: 510 pounds
Steps:
1. Labor Cost:
[tex]\[ \text{Labor Cost} = 5 \times 40 \times 16 = 3200 \text{ dollars} \][/tex]
2. Overhead Cost:
[tex]\[ \text{Overhead Cost} = 1.5 \times 3200 = 4800 \text{ dollars} \][/tex]
3. Material Cost:
[tex]\[ \text{Material Cost} = 510 \times 9 = 4590 \text{ dollars} \][/tex]
4. Total Input Costs:
[tex]\[ \text{Total Input Costs} = 3200 + 4800 + 4590 = 12590 \text{ dollars} \][/tex]
5. MFP:
[tex]\[ \text{MFP} = \frac{36000}{12590} \approx 2.86 \][/tex]
### Week 3:
Given:
- Output: 29,000 units
- Workers: 7
- Material: 490 pounds
Steps:
1. Labor Cost:
[tex]\[ \text{Labor Cost} = 7 \times 40 \times 16 = 4480 \text{ dollars} \][/tex]
2. Overhead Cost:
[tex]\[ \text{Overhead Cost} = 1.5 \times 4480 = 6720 \text{ dollars} \][/tex]
3. Material Cost:
[tex]\[ \text{Material Cost} = 490 \times 9 = 4410 \text{ dollars} \][/tex]
4. Total Input Costs:
[tex]\[ \text{Total Input Costs} = 4480 + 6720 + 4410 = 15610 \text{ dollars} \][/tex]
5. MFP:
[tex]\[ \text{MFP} = \frac{29000}{15610} \approx 1.86 \][/tex]
### Week 4:
Given:
- Output: 39,000 units
- Workers: 7
- Material: 590 pounds
Steps:
1. Labor Cost:
[tex]\[ \text{Labor Cost} = 7 \times 40 \times 16 = 4480 \text{ dollars} \][/tex]
2. Overhead Cost:
[tex]\[ \text{Overhead Cost} = 1.5 \times 4480 = 6720 \text{ dollars} \][/tex]
3. Material Cost:
[tex]\[ \text{Material Cost} = 590 \times 9 = 5310 \text{ dollars} \][/tex]
4. Total Input Costs:
[tex]\[ \text{Total Input Costs} = 4480 + 6720 + 5310 = 16510 \text{ dollars} \][/tex]
5. MFP:
[tex]\[ \text{MFP} = \frac{39000}{16510} \approx 2.36 \][/tex]
Summarizing the MFP results:
[tex]\[ \begin{array}{|c|c|} \hline \text{Week} & \text{MFP} \\ \hline 1 & 2.94 \\ \hline 2 & 2.86 \\ \hline 3 & 1.86 \\ \hline 4 & 2.36 \\ \hline \end{array} \][/tex]
1. Calculate the total labor cost.
2. Calculate the overhead cost.
3. Calculate the material cost.
4. Sum the total input costs (labor, overhead, and material costs).
5. Compute the MFP by dividing the output by the total input costs.
6. Round the MFP values to two decimal places.
### Week 1:
Given:
- Output: 31,000 units
- Workers: 4
- Material: 460 pounds
Steps:
1. Labor Cost:
[tex]\[ \text{Labor Cost} = \text{Workers} \times \text{Hours per Week} \times \text{Hourly Wage} = 4 \times 40 \times 16 = 2560 \text{ dollars} \][/tex]
2. Overhead Cost:
[tex]\[ \text{Overhead Cost} = 1.5 \times \text{Labor Cost} = 1.5 \times 2560 = 3840 \text{ dollars} \][/tex]
3. Material Cost:
[tex]\[ \text{Material Cost} = \text{Material} \times \text{Material Cost per Pound} = 460 \times 9 = 4140 \text{ dollars} \][/tex]
4. Total Input Costs:
[tex]\[ \text{Total Input Costs} = \text{Labor Cost} + \text{Overhead Cost} + \text{Material Cost} = 2560 + 3840 + 4140 = 10540 \text{ dollars} \][/tex]
5. MFP:
[tex]\[ \text{MFP} = \frac{\text{Output}}{\text{Total Input Costs}} = \frac{31000}{10540} \approx 2.94 \][/tex]
### Week 2:
Given:
- Output: 36,000 units
- Workers: 5
- Material: 510 pounds
Steps:
1. Labor Cost:
[tex]\[ \text{Labor Cost} = 5 \times 40 \times 16 = 3200 \text{ dollars} \][/tex]
2. Overhead Cost:
[tex]\[ \text{Overhead Cost} = 1.5 \times 3200 = 4800 \text{ dollars} \][/tex]
3. Material Cost:
[tex]\[ \text{Material Cost} = 510 \times 9 = 4590 \text{ dollars} \][/tex]
4. Total Input Costs:
[tex]\[ \text{Total Input Costs} = 3200 + 4800 + 4590 = 12590 \text{ dollars} \][/tex]
5. MFP:
[tex]\[ \text{MFP} = \frac{36000}{12590} \approx 2.86 \][/tex]
### Week 3:
Given:
- Output: 29,000 units
- Workers: 7
- Material: 490 pounds
Steps:
1. Labor Cost:
[tex]\[ \text{Labor Cost} = 7 \times 40 \times 16 = 4480 \text{ dollars} \][/tex]
2. Overhead Cost:
[tex]\[ \text{Overhead Cost} = 1.5 \times 4480 = 6720 \text{ dollars} \][/tex]
3. Material Cost:
[tex]\[ \text{Material Cost} = 490 \times 9 = 4410 \text{ dollars} \][/tex]
4. Total Input Costs:
[tex]\[ \text{Total Input Costs} = 4480 + 6720 + 4410 = 15610 \text{ dollars} \][/tex]
5. MFP:
[tex]\[ \text{MFP} = \frac{29000}{15610} \approx 1.86 \][/tex]
### Week 4:
Given:
- Output: 39,000 units
- Workers: 7
- Material: 590 pounds
Steps:
1. Labor Cost:
[tex]\[ \text{Labor Cost} = 7 \times 40 \times 16 = 4480 \text{ dollars} \][/tex]
2. Overhead Cost:
[tex]\[ \text{Overhead Cost} = 1.5 \times 4480 = 6720 \text{ dollars} \][/tex]
3. Material Cost:
[tex]\[ \text{Material Cost} = 590 \times 9 = 5310 \text{ dollars} \][/tex]
4. Total Input Costs:
[tex]\[ \text{Total Input Costs} = 4480 + 6720 + 5310 = 16510 \text{ dollars} \][/tex]
5. MFP:
[tex]\[ \text{MFP} = \frac{39000}{16510} \approx 2.36 \][/tex]
Summarizing the MFP results:
[tex]\[ \begin{array}{|c|c|} \hline \text{Week} & \text{MFP} \\ \hline 1 & 2.94 \\ \hline 2 & 2.86 \\ \hline 3 & 1.86 \\ \hline 4 & 2.36 \\ \hline \end{array} \][/tex]
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