The per unit standard for direct materials are 5 gallons at three dollars per gallon last month 20,000 gallons of direct materials that actually costed 60,000 were used to produce 10,000 units of product. What is the materials quantity variance?

To calculate the **materials quantity variance**, we need to follow these steps:

### Step 1: Gather the necessary information.
- **Standard quantity per unit** = 5 gallons
- **Standard price per gallon** = $3
- **Actual quantity used** = 20,000 gallons
- **Actual output produced** = 10,000 units

### Step 2: Calculate the **standard quantity allowed** for actual production.
The standard quantity allowed is the number of units produced multiplied by the standard quantity of materials per unit:

\[
\text{Standard quantity allowed} = \text{Actual units produced} \times \text{Standard quantity per unit}
\]

\[
\text{Standard quantity allowed} = 10,000 \times 5 = 50,000 \text{ gallons}
\]

### Step 3: Calculate the **materials quantity variance**.
The formula for materials quantity variance is:

\[
\text{Materials quantity variance} = (\text{Standard quantity allowed} - \text{Actual quantity used}) \times \text{Standard price}
\]

Substitute the known values:

\[
\text{Materials quantity variance} = (50,000 - 20,000) \times 3 = 30,000 \times 3 = 90,000
\]

### Step 4: Interpret the variance.
Since the actual quantity used (20,000 gallons) is **less than** the standard quantity allowed (50,000 gallons), the variance is **favorable**.

\[
\text{Materials quantity variance} = \$90,000 \text{ Favorable (F)}
\]

### Conclusion:
The materials quantity variance is **$90,000 Favorable**.

---

Do you want more details or have any questions? Here are 5 related questions to expand your understanding:

1. What is the formula for materials price variance, and how does it differ from quantity variance?
2. Can the materials quantity variance ever be unfavorable? If so, when?
3. How does materials quantity variance impact overall production costs?
4. What factors could cause a favorable materials quantity variance?
5. What is the total materials variance, combining price and quantity variances?

**Tip**: Favorable variances occur when actual costs or usage are less than the standard, while unfavorable variances occur when actuals exceed the standard.

Learn how to calculate the materials quantity variance for direct materials in production. This example uses 10,000 units produced with 20,000 gallons of materials consumed, providing a step-by-step guide to variance analysis in cost accounting. Suitable for college-level accounting and business studies.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation