Final answer:
The labor efficiency variance for Model ZX40 is calculated to be $1,450 favorable, as fewer hours were worked than expected. The labor rate variance is computed as $4,100 unfavorable due to higher actual labor costs compared to standard. The provided options in the question do not match these calculations, indicating a possible error in the options.
Step-by-step explanation:
To calculate labor variances, we need to look at both the labor efficiency variance and the labor rate variance. The labor efficiency variance is the difference between what the actual hours worked should have cost based on standard labor hours and what they did cost at the standard rate. The labor rate variance is the difference between what the actual labor cost was at the standard rate and what it actually cost.
The standard cost for direct labor to manufacture one unit of Model ZX40 is 0.5 hours at a rate of $14.50 per hour. Therefore, the standard cost to produce one unit is 0.5 hours × $14.50/hour = $7.25.
To find the labor efficiency variance, first calculate the standard labor hours for actual production: 4,600 units × 0.5 hours/unit = 2,300 standard hours. The actual hours worked were 2,200, so the difference is 2,300 - 2,200 = 100 hours. Multiply this by the standard rate of $14.50 to find the variance: 100 hours × $14.50/hour = $1,450 favorable, because less hours were worked than expected.
For the labor rate variance, we look at the actual cost versus the expected cost at standard rate: Actual cost ($36,000) - (2,200 hours × $14.50/hour) = Actual cost - $31,900 = $4,100 unfavorable.
The correct option from the given choices would be:
Labor Efficiency Variance: $1,450 Favorable; Labor Rate Variance: $4,100 Unfavorable
However, none of the listed options match this correct calculation, so we must advise the student that there could be an error in the provided options.