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To calculate the labor rate variance (LRV) and labor efficiency variance (LEV) for August, let's follow these steps:
1. Calculate the standard direct labor cost for actual production:
- The standard labor time per unit is \(0.5\) hours.
- The standard labor rate per hour is \( \$ 23.6 \).
- The actual production in August was \(21870\) units.
[tex]\[ \text{Standard hours for actual production} = \text{actual production units} \times \text{standard labor time per unit} \][/tex]
[tex]\[ \text{Standard hours for actual production} = 21870 \text{ units} \times 0.5 \text{ hours/unit} = 10935 \text{ hours} \][/tex]
[tex]\[ \text{Standard cost for actual production} = \text{Standard hours for actual production} \times \text{standard labor rate per hour} \][/tex]
[tex]\[ \text{Standard cost for actual production} = 10935 \text{ hours} \times \[tex]$23.6/\text{hour} = \$[/tex]257,556
\][/tex]
2. Calculate the Labor Rate Variance (LRV):
- The actual labor rate per hour is \( \$ 11.20 \).
- The standard labor rate per hour is \( \$ 23.6 \).
- The actual direct labor hours were \(9720\).
[tex]\[ \text{Labor Rate Variance (LRV)} = (\text{actual labor rate per hour} - \text{standard labor rate per hour}) \times \text{actual direct labor hours} \][/tex]
[tex]\[ \text{Labor Rate Variance (LRV)} = (\[tex]$11.20 - \$[/tex]23.6) \times 9720 \text{ hours}
\][/tex]
[tex]\[ \text{Labor Rate Variance (LRV)} = (-\[tex]$12.4) \times 9720 \text{ hours} = -\$[/tex]120,528
\][/tex]
Since LRV is negative, it is favorable (F).
3. Calculate the actual labor cost should have been:
- The actual direct labor hours were \(9720\).
- The standard labor rate per hour is \( \$ 23.6 \).
[tex]\[ \text{Standard labor cost for actual hours worked} = \text{actual direct labor hours} \times \text{standard labor rate per hour} \][/tex]
[tex]\[ \text{Standard labor cost for actual hours worked} = 9720 \text{ hours} \times \[tex]$23.6/\text{hour} = \$[/tex]229,792
\][/tex]
4. Calculate the Labor Efficiency Variance (LEV):
- The actual direct labor hours were \(9720\).
- The standard hours for actual production were \(10935\).
- The standard labor rate per hour is \( \$ 23.6 \).
[tex]\[ \text{Labor Efficiency Variance (LEV)} = (\text{actual direct labor hours} - \text{standard hours for actual production}) \times \text{standard labor rate per hour} \][/tex]
[tex]\[ \text{Labor Efficiency Variance (LEV)} = (9720 \text{ hours} - 10935 \text{ hours}) \times \$23.6/\text{hour} \][/tex]
[tex]\[ \text{Labor Efficiency Variance (LEV)} = (-1215 \text{ hours}) \times \[tex]$23.6/\text{hour} = -\$[/tex]28,674
\][/tex]
Since LEV is negative, it is favorable (F).
### Final Answer:
[tex]\[ \begin{array}{|l|l|l|} \hline \text{Labor rate variance} & -\$120,528 & \text{F} \\ \hline \text{Labor efficiency variance} & -\$28,674 & \text{F} \\ \hline \end{array} \][/tex]
1. Calculate the standard direct labor cost for actual production:
- The standard labor time per unit is \(0.5\) hours.
- The standard labor rate per hour is \( \$ 23.6 \).
- The actual production in August was \(21870\) units.
[tex]\[ \text{Standard hours for actual production} = \text{actual production units} \times \text{standard labor time per unit} \][/tex]
[tex]\[ \text{Standard hours for actual production} = 21870 \text{ units} \times 0.5 \text{ hours/unit} = 10935 \text{ hours} \][/tex]
[tex]\[ \text{Standard cost for actual production} = \text{Standard hours for actual production} \times \text{standard labor rate per hour} \][/tex]
[tex]\[ \text{Standard cost for actual production} = 10935 \text{ hours} \times \[tex]$23.6/\text{hour} = \$[/tex]257,556
\][/tex]
2. Calculate the Labor Rate Variance (LRV):
- The actual labor rate per hour is \( \$ 11.20 \).
- The standard labor rate per hour is \( \$ 23.6 \).
- The actual direct labor hours were \(9720\).
[tex]\[ \text{Labor Rate Variance (LRV)} = (\text{actual labor rate per hour} - \text{standard labor rate per hour}) \times \text{actual direct labor hours} \][/tex]
[tex]\[ \text{Labor Rate Variance (LRV)} = (\[tex]$11.20 - \$[/tex]23.6) \times 9720 \text{ hours}
\][/tex]
[tex]\[ \text{Labor Rate Variance (LRV)} = (-\[tex]$12.4) \times 9720 \text{ hours} = -\$[/tex]120,528
\][/tex]
Since LRV is negative, it is favorable (F).
3. Calculate the actual labor cost should have been:
- The actual direct labor hours were \(9720\).
- The standard labor rate per hour is \( \$ 23.6 \).
[tex]\[ \text{Standard labor cost for actual hours worked} = \text{actual direct labor hours} \times \text{standard labor rate per hour} \][/tex]
[tex]\[ \text{Standard labor cost for actual hours worked} = 9720 \text{ hours} \times \[tex]$23.6/\text{hour} = \$[/tex]229,792
\][/tex]
4. Calculate the Labor Efficiency Variance (LEV):
- The actual direct labor hours were \(9720\).
- The standard hours for actual production were \(10935\).
- The standard labor rate per hour is \( \$ 23.6 \).
[tex]\[ \text{Labor Efficiency Variance (LEV)} = (\text{actual direct labor hours} - \text{standard hours for actual production}) \times \text{standard labor rate per hour} \][/tex]
[tex]\[ \text{Labor Efficiency Variance (LEV)} = (9720 \text{ hours} - 10935 \text{ hours}) \times \$23.6/\text{hour} \][/tex]
[tex]\[ \text{Labor Efficiency Variance (LEV)} = (-1215 \text{ hours}) \times \[tex]$23.6/\text{hour} = -\$[/tex]28,674
\][/tex]
Since LEV is negative, it is favorable (F).
### Final Answer:
[tex]\[ \begin{array}{|l|l|l|} \hline \text{Labor rate variance} & -\$120,528 & \text{F} \\ \hline \text{Labor efficiency variance} & -\$28,674 & \text{F} \\ \hline \end{array} \][/tex]
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