Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
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]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
