To calculate the standard labor variances, we will use the following formulas:

1. Labour Rate Variance (LRV): $\text{LRV} = (\text{Actual Rate} - \text{Standard Rate}) \times \text{Actual Hours Worked}$

2. Labour Efficiency Variance (LEV): $\text{LEV} = (\text{Actual Hours Worked} - \text{Standard Hours for Actual Output}) \times \text{Standard Rate}$

Step 1: Calculate total standard hours

For the actual output of 1,000 units, the standard hours for each category of labor (Skilled, Semi-skilled, Unskilled) can be calculated using their standard hour rates:

• Skilled: 2 hours per unit × 1,000 units = 2,000 standard hours
• Semi-skilled: 3 hours per unit × 1,000 units = 3,000 standard hours
• Unskilled: 5 hours per unit × 1,000 units = 5,000 standard hours

Thus, Total Standard Hours = 2,000 + 3,000 + 5,000 = 10,000 hours.

Step 2: Adjust actual hours for idle time

We were given that the total hours paid included 1,000 idle hours broken down as follows:

• Skilled idle hours: 500
• Semi-skilled idle hours: 400
• Unskilled idle hours: $1,000 - (500 + 400) = 100$

Therefore, the actual hours worked are:

• Skilled: 9,000 - 500 = 8,500 hours
• Semi-skilled: 17,000 - 400 = 16,600 hours
• Unskilled: 30,000 - 100 = 29,900 hours

Step 3: Calculate Labor Rate Variance (LRV)

Using the formula $\text{LRV} = (\text{Actual Rate} - \text{Standard Rate}) \times \text{Actual Hours Worked}$:

• Skilled: $(7 - 5) \times 8,500 = 2 \times 8,500 = 17,000 (Unfavorable)$

• Semi-skilled: $(2.75 - 3) \times 16,600 = -0.25 \times 16,600 = -4,150 (Favorable)$

• Unskilled: $(1.5 - 2) \times 29,900 = -0.5 \times 29,900 = -14,950 (Favorable)$

Total Labour Rate Variance = 17,000 (U) - 4,150 (F) - 14,950 (F) = $\mathbf{-2,100}$ (Favorable)

Step 4: Calculate Labour Efficiency Variance (LEV)

Using the formula $\text{LEV} = (\text{Actual Hours Worked} - \text{Standard Hours}) \times \text{Standard Rate}$:

• Skilled: $(8,500 - 2,000) \times 5 = 6,500 \times 5 = 32,500 (Unfavorable)$

• Semi-skilled: $(16,600 - 3,000) \times 3 = 13,600 \times 3 = 40,800 (Unfavorable)$

• Unskilled: $(29,900 - 5,000) \times 2 = 24,900 \times 2 = 49,800 (Unfavorable)$

Total Labour Efficiency Variance = 32,500 + 40,800 + 49,800 = $\mathbf{123,100}$ (Unfavorable)

Step 5: Total Labour Variance

The Total Labour Variance is the sum of the Labour Rate Variance and the Labour Efficiency Variance:

$\text{Total Labour Variance} = \text{LRV} + \text{LEV} = (-2,100) + 123,100 = \mathbf{121,000} \ (\text{Unfavorable})$

Summary of Variances:

• Labour Rate Variance: $\mathbf{-2,100}$ (Favorable)
• Labour Efficiency Variance: $\mathbf{123,100}$ (Unfavorable)
• Total Labour Variance: $\mathbf{121,000}$ (Unfavorable)

Would you like to explore more details or have any questions?

Here are 5 questions you could explore next:

1. What are the causes of favorable and unfavorable labor variances?
2. How can a company improve labor efficiency to reduce unfavorable variances?
3. What are the differences between idle time variance and efficiency variance?
4. How does labor variance impact overall profitability?
5. How are labor variances integrated into a company's budgeting process?

Tip: Tracking and analyzing variances regularly can help identify inefficiencies in production early on and lead to cost-saving improvements.