To answer these questions, let's analyze each one using the data given.

1. Standard Price for One Unit of Material

The standard cost for material output was provided as $100,000, which was intended for the August production of 10,000 benches. Since each bench requires 5 feet of material, we can calculate the total feet required at the standard cost rate: $10,000 \text{ benches} \times 5 \text{ feet per bench} = 50,000 \text{ feet of material}$ Therefore, the standard price per foot of material is: $\frac{\text{Standard Cost for Material Output}}{\text{Total Standard Material Quantity Required}} = \frac{100,000}{50,000} = 2 \text{ dollars per foot}$

Answer: The standard price for one unit of material is $2 per foot.

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2. Total Number of Units of Material Used to Produce the August Output

We know that there was an unfavorable direct materials quantity variance of $6,000, which suggests that more material was used than the standard amount of 50,000 feet for 10,000 benches.

The quantity variance formula is: $\text{Direct Materials Quantity Variance} = (\text{Actual Quantity Used} - \text{Standard Quantity Allowed}) \times \text{Standard Price}$ Rearranging to solve for the actual quantity used: $\text{Actual Quantity Used} = \frac{\text{Direct Materials Quantity Variance}}{\text{Standard Price}} + \text{Standard Quantity Allowed}$ Plugging in the values: $\text{Actual Quantity Used} = \frac{6,000}{2} + 50,000 = 3,000 + 50,000 = 53,000 \text{ feet}$

Answer: The total number of units of material used in August was 53,000 feet.

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3. Direct Materials Price Variance for August

The direct materials price variance formula is: $\text{Direct Materials Price Variance} = (\text{Actual Price} - \text{Standard Price}) \times \text{Actual Quantity Used}$ The total cost of 60,000 feet purchased was $300,000, giving an actual price per foot of: $\frac{300,000}{60,000} = 5 \text{ dollars per foot}$ Thus, the price variance is: $(5 - 2) \times 53,000 = 3 \times 53,000 = 159,000$

Answer: The direct materials price variance for August was $159,000 (unfavorable).

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Summary of Answers:

1. Standard price for one unit of material: $2 per foot
2. Total number of units of material used to produce August output: 53,000 feet
3. Direct materials price variance for August: $159,000 (unfavorable)

Would you like further details on any of these calculations, or do you have any questions?

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Further Questions

1. What would be the impact if the material variance were favorable instead?
2. How does the standard costing method help in variance analysis?
3. How could April Industries improve its direct materials cost efficiency?
4. What are potential causes of an unfavorable price variance in raw materials?
5. How would a change in the standard cost per unit affect the total variances?

Tip: Always compare both quantity and price variances separately to pinpoint where costs deviate from standards.