Final answer:
The variable overhead rate variance is calculated as the difference between the actual overhead cost and the standard overhead expected for the actual output. The variance is found to be $12,970 unfavorable, which does not match any of the answer choices provided.
Step-by-step explanation:
To calculate the variable overhead rate variance, we need to compare the actual overhead incurred to the standard overhead expected for the actual production levels. First, we calculate the standard overhead cost that should have been incurred for the actual output by multiplying the standard hours permitted for actual production (8.0 hours per unit) by the standard variable overhead rate ($14.40 per hour) and the number of actual units produced (200 units). This gives us a total of $28,800 (8 hours x $14.40 x 200 units) as the standard cost.
Next, we subtract the actual variable manufacturing overhead cost ($41,770) from the standard cost to find the variance. The variance is $41,770 - $28,800 = $12,970 unfavorable, because the actual cost is higher than the standard cost. However, none of the provided answer choices ($730 F, $18,000 F, $18,000 U, $730 U) match this calculated variance.