The direct materials quantity variance measures the difference between the actual quantity of materials used in production and the standard quantity allowed, multiplied by the standard cost per unit. Here's how to calculate it:

Step 1: Find the standard quantity allowed

The standard quantity of materials allowed is based on the number of units produced and the per unit standard for direct materials. In this case:

• 6,000 units were produced.
• The standard is 3 gallons per unit.

So, the standard quantity allowed = $6,000 \, \text{units} \times 3 \, \text{gallons/unit} = 18,000 \, \text{gallons}$.

Step 2: Identify the actual quantity used

The actual quantity used was 11,000 gallons.

Step 3: Calculate the quantity variance

The direct materials quantity variance formula is:

$\text{Quantity Variance} = (\text{Actual Quantity Used} - \text{Standard Quantity Allowed}) \times \text{Standard Cost per Unit}$

$\text{Quantity Variance} = (11,000 \, \text{gallons} - 18,000 \, \text{gallons}) \times 5 \, \text{dollars/gallon}$

$\text{Quantity Variance} = (-7,000 \, \text{gallons}) \times 5 \, \text{dollars/gallon}$

$\text{Quantity Variance} = -35,000 \, \text{dollars}$

Conclusion:

The direct materials quantity variance is $35,000 favorable because the actual quantity used was less than the standard quantity allowed.

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:

1. What is the price variance for the direct materials used in this scenario?
2. How would the variance change if more materials had been used than the standard allowed?
3. How can a company use quantity variance to improve operational efficiency?
4. What other variances might impact the overall cost variance for this product?
5. How do you calculate the direct labor quantity variance in a similar situation?

Tip: A favorable variance occurs when actual costs or quantities are lower than expected, while an unfavorable variance occurs when they are higher.