Answer :
To compute the plantwide overhead rate, we need to follow a series of steps, which include determining the total direct labor hours needed for each product and then calculating the plantwide overhead rate based on those hours.
### Step-by-Step Solution
1. Determine Direct Labor Hours Per Unit:
- The direct labor cost per hour is given as \$28.
- For CC1, the direct labor cost per unit is \$22.40.
- For CC2, the direct labor cost per unit is \$15.40.
We need to convert the labor cost per unit into direct labor hours per unit by dividing the direct labor cost per unit by the direct labor cost per hour.
For CC1:
[tex]\[ \text{Direct Labor Hours per Unit (CC1)} = \frac{\[tex]$22.40}{\$[/tex]28 \text{ per hour}} = 0.8 \text{ hours per unit}
\][/tex]
For CC2:
[tex]\[ \text{Direct Labor Hours per Unit (CC2)} = \frac{\[tex]$15.40}{\$[/tex]28 \text{ per hour}} = 0.55 \text{ hours per unit}
\][/tex]
2. Calculate Total Direct Labor Hours:
- The company expects to manufacture 22,000 units of CC1 and 91,000 units of CC2 next year.
Total direct labor hours for each product can be calculated by multiplying the direct labor hours per unit by the number of units to be manufactured.
For CC1:
[tex]\[ \text{Total Direct Labor Hours for CC1} = 0.8 \text{ hours per unit} \times 22,000 \text{ units} = 17,600 \text{ hours} \][/tex]
For CC2:
[tex]\[ \text{Total Direct Labor Hours for CC2} = 0.55 \text{ hours per unit} \times 91,000 \text{ units} = 50,050 \text{ hours} \][/tex]
3. Compute Total Direct Labor Hours:
- Add the total direct labor hours for CC1 and CC2 to get the overall direct labor hours.
[tex]\[ \text{Total Direct Labor Hours} = 17,600 \text{ hours (CC1)} + 50,050 \text{ hours (CC2)} = 67,650 \text{ hours} \][/tex]
4. Compute the Plantwide Overhead Rate:
- The plantwide overhead is estimated to be \$338,250.
- The plantwide overhead rate is calculated by dividing the total overhead by the total direct labor hours.
[tex]\[ \text{Plantwide Overhead Rate} = \frac{\[tex]$338,250}{67,650 \text{ hours}} = \$[/tex]5 \text{ per direct labor hour}
\][/tex]
### Conclusion
After following the above steps, we have determined that the plantwide overhead rate for next year will be [tex]\(\boxed{5}\)[/tex] dollars per direct labor hour.
### Step-by-Step Solution
1. Determine Direct Labor Hours Per Unit:
- The direct labor cost per hour is given as \$28.
- For CC1, the direct labor cost per unit is \$22.40.
- For CC2, the direct labor cost per unit is \$15.40.
We need to convert the labor cost per unit into direct labor hours per unit by dividing the direct labor cost per unit by the direct labor cost per hour.
For CC1:
[tex]\[ \text{Direct Labor Hours per Unit (CC1)} = \frac{\[tex]$22.40}{\$[/tex]28 \text{ per hour}} = 0.8 \text{ hours per unit}
\][/tex]
For CC2:
[tex]\[ \text{Direct Labor Hours per Unit (CC2)} = \frac{\[tex]$15.40}{\$[/tex]28 \text{ per hour}} = 0.55 \text{ hours per unit}
\][/tex]
2. Calculate Total Direct Labor Hours:
- The company expects to manufacture 22,000 units of CC1 and 91,000 units of CC2 next year.
Total direct labor hours for each product can be calculated by multiplying the direct labor hours per unit by the number of units to be manufactured.
For CC1:
[tex]\[ \text{Total Direct Labor Hours for CC1} = 0.8 \text{ hours per unit} \times 22,000 \text{ units} = 17,600 \text{ hours} \][/tex]
For CC2:
[tex]\[ \text{Total Direct Labor Hours for CC2} = 0.55 \text{ hours per unit} \times 91,000 \text{ units} = 50,050 \text{ hours} \][/tex]
3. Compute Total Direct Labor Hours:
- Add the total direct labor hours for CC1 and CC2 to get the overall direct labor hours.
[tex]\[ \text{Total Direct Labor Hours} = 17,600 \text{ hours (CC1)} + 50,050 \text{ hours (CC2)} = 67,650 \text{ hours} \][/tex]
4. Compute the Plantwide Overhead Rate:
- The plantwide overhead is estimated to be \$338,250.
- The plantwide overhead rate is calculated by dividing the total overhead by the total direct labor hours.
[tex]\[ \text{Plantwide Overhead Rate} = \frac{\[tex]$338,250}{67,650 \text{ hours}} = \$[/tex]5 \text{ per direct labor hour}
\][/tex]
### Conclusion
After following the above steps, we have determined that the plantwide overhead rate for next year will be [tex]\(\boxed{5}\)[/tex] dollars per direct labor hour.
