To solve for the variable overhead rate variance, we can follow a series of steps using the given data:
### Step 1: Determine the actual variable overhead rate
First, we need to determine the actual variable overhead rate for the month using the actual total variable manufacturing overhead cost and the actual hours worked:
[tex]\[
\text{Actual Variable Overhead Rate} = \frac{\text{Actual Total Variable Overhead Cost}}{\text{Actual Hours}}
\][/tex]
Given:
- Actual total variable overhead cost = \[tex]$31,330
- Actual hours = 2,600 hours
\[
\text{Actual Variable Overhead Rate} = \frac{31,330}{2,600} = 12.05 \text{ per hour}
\]
### Step 2: Calculate the standard cost for the actual hours worked
Next, calculate the standard variable overhead cost based on the actual hours worked and the standard variable overhead rate:
\[
\text{Standard Cost} = \text{Actual Hours} \times \text{Standard Variable Overhead Rate}
\]
Given:
- Actual hours = 2,600 hours
- Standard variable overhead rate = \$[/tex]12.00 per hour
[tex]\[
\text{Standard Cost} = 2,600 \times 12.00 = 31,200.00
\][/tex]
### Step 3: Calculate the variable overhead rate variance
Finally, calculate the variable overhead rate variance by subtracting the standard cost from the actual total variable overhead cost:
[tex]\[
\text{Variable Overhead Rate Variance} = \text{Actual Total Variable Overhead Cost} - \text{Standard Cost}
\][/tex]
Given:
- Actual total variable overhead cost = \[tex]$31,330
- Standard cost = \$[/tex]31,200
[tex]\[
\text{Variable Overhead Rate Variance} = 31,330 - 31,200 = 130
\][/tex]
Since the actual cost is higher than the standard cost, the variance is unfavorable (U).
So, the variable overhead rate variance for the month is:
[tex]\[
\$130 \text{ U}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\$130 \text{ U}}
\][/tex]
Thus, the variable overhead rate variance is \[tex]$130 unfavorable, indicated by option B) \$[/tex]130 U.
