Final answer:
The variable-overhead efficiency variance can be calculated by multiplying the standard variable overhead rate per machine hour by the difference between the standard hours allowed and the actual hours worked. For the given scenario, the variable-overhead efficiency variance is $27,000 favorable.
Step-by-step explanation:
The variable-overhead efficiency variance can be calculated by multiplying the standard variable overhead rate per machine hour by the difference between the standard hours allowed and the actual hours worked.
Given that the standard variable overhead rate is $4.50 per machine hour and the standard time allowed per unit is 3 hours, the total standard hours allowed for the actual units produced of 42,000 would be 42,000 x 3 = 126,000 hours.
The actual machine hours worked is 120,000 hours. Therefore, the variable-overhead efficiency variance is (126,000 - 120,000) x $4.50 = $27,000 favorable (Option C).