Final answer:
Luke's actual variable overhead cost is B. $280,500. It was calculated by adjusting the standard cost of $292,500 with the given efficiency and spending variances.
Step-by-step explanation:
To find Luke's actual variable overhead during the period, we need to factor in the standard cost, the efficiency variance, and the spending variance. The efficiency variance tells us how much more or less was spent due to efficiency or inefficiency in using the machine hours compared to the standard, and the spending variance indicates how much more or less was spent due to the actual price per machine hour differing from the standard cost.
The standard cost for the actual production is calculated by multiplying the actual units produced by the standard machine hours per unit and the standard overhead rate per machine hour. Thus:
- Actual units produced: 19,500 units
- Standard machine hours per unit: 3 hours
- Standard variable overhead rate: $5 per machine hour
Standard cost = 19,500 units * 3 hours/unit * $5/hour = $292,500
The actual variable overhead cost is then adjusted by adding the unfavorable efficiency variance (since more was spent due to inefficiency) and subtracting the favorable spending variance (since less was spent due to a lower actual price):
Actual variable overhead cost = Standard cost + Efficiency variance - Spending variance
Actual variable overhead cost = $292,500 + $9,000 (unfavorable) - $21,000 (favorable)
Actual variable overhead cost = $292,500 + $9,000 - $21,000 = $280,500
Therefore, the correct answer is B. $280,500.