Let's solve this step-by-step.
1. Calculate total manufacturing overhead costs:
The estimated manufacturing overhead costs for Department 1 are \[tex]$2,530,000 and for Department 2 are \$[/tex]900,000.
[tex]\[
\text{Total manufacturing overhead costs} = \$2,530,000 + \$900,000 = \$3,430,000
\][/tex]
2. Calculate total direct labor hours (DLH):
The estimated direct labor hours for Department 1 are 168,000 hours and for Department 2 are 110,000 hours.
[tex]\[
\text{Total direct labor hours} = 168,000 \text{ DLH} + 110,000 \text{ DLH} = 278,000 \text{ DLH}
\][/tex]
3. Calculate the plantwide overhead rate:
The plantwide overhead rate is calculated by dividing the total manufacturing overhead costs by the total direct labor hours.
[tex]\[
\text{Plantwide overhead rate} = \frac{\text{Total manufacturing overhead costs}}{\text{Total direct labor hours}} = \frac{\$3,430,000}{278,000 \text{ DLH}} = \$12.34 \text{ per DLH}
\][/tex]
4. Calculate total direct labor hours needed for the expected production:
The company expects to produce 400,000 units, with each unit requiring 0.90 direct labor hours.
[tex]\[
\text{Total direct labor hours needed} = 400,000 \text{ units} \times 0.90 \text{ DLH/unit} = 360,000 \text{ DLH}
\][/tex]
5. Calculate overhead assigned to each unit:
First, we find the overhead per unit based on the labor hours each unit requires and the plantwide overhead rate.
[tex]\[
\text{Overhead assigned to each unit} = 0.90 \text{ DLH/unit} \times \$12.34 \text{ per DLH} = \$11.11 \text{ per unit}
\][/tex]
Therefore, the amount of overhead assigned to each unit produced is \[tex]$11.11 per unit.
The correct answer from the options is:
\[
\$[/tex]11.11 \text{ per unit}
\]
