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Sagot :
Certainly! Let's go through a step-by-step solution to analyze the variable cost of goods sold and understand where the problem may be lying.
### Step-by-step Analysis:
1. Calculate Total Amount Spent on Materials:
- Material Purchased: 21,500 pounds
- Actual Cost per Pound: [tex]$3.25 \[ \text{Total Material Cost} = \text{Material Purchased} \times \text{Actual Cost per Pound} \] \[ \text{Total Material Cost} = 21,500 \times 3.25 = \$[/tex]69,875
\]
2. Calculate Standard Material Cost for Actual Production:
- Pools Produced: 5,000
- Standard Material Pounds per Pool: 3.3
- Standard Cost per Pound: [tex]$2.80 \[ \text{Standard Total Material Pounds} = \text{Pools Produced} \times \text{Standard Material Pounds per Pool} \] \[ \text{Standard Total Material Pounds} = 5,000 \times 3.3 = 16,500 \, \text{pounds} \] \[ \text{Standard Total Material Cost} = \text{Standard Total Material Pounds} \times \text{Standard Cost per Pound} \] \[ \text{Standard Total Material Cost} = 16,500 \times 2.80 = \$[/tex]46,200
\]
3. Calculate Material Price Variance:
- Actual Material Used: 16,300 pounds
- Actual Cost per Pound: [tex]$3.25 - Standard Cost per Pound: $[/tex]2.80
[tex]\[ \text{Material Price Variance} = (\text{Actual Cost per Pound} - \text{Standard Cost per Pound}) \times \text{Actual Material Used} \][/tex]
[tex]\[ \text{Material Price Variance} = (3.25 - 2.80) \times 16,300 = 0.45 \times 16,300 = \$7,335 \][/tex]
4. Calculate Material Quantity Variance:
- Actual Material Used: 16,300 pounds
- Standard Total Material Pounds for Production: 16,500 pounds
- Standard Cost per Pound: [tex]$2.80 \[ \text{Material Quantity Variance} = (\text{Actual Material Used} - \text{Standard Total Material Pounds}) \times \text{Standard Cost per Pound} \] \[ \text{Material Quantity Variance} = (16,300 - 16,500) \times 2.80 = -200 \times 2.80 = -\$[/tex]560
\]
5. Calculate Total Material Variance:
[tex]\[ \text{Total Material Variance} = \text{Material Price Variance} + \text{Material Quantity Variance} \][/tex]
[tex]\[ \text{Total Material Variance} = 7,335 + (-560) = \$6,775 \][/tex]
### Summary of Findings:
- Total Material Cost: [tex]$69,875 - Standard Total Material Cost: $[/tex]46,200
- Material Price Variance: [tex]$7,335 - Material Quantity Variance: -$[/tex]560
- Total Material Variance: $6,775
### Conclusion:
The direct materials' actual cost is significantly higher than the standard cost, primarily due to the price variance. This means that the primary issue is with the price being paid for the materials, which is higher than the standard expected rate. Additionally, there is a slight efficiency in the quantity of materials used, as seen in the negative quantity variance. Overall, Ms. Dunn should focus on negotiating better prices for materials to bring the variable cost of goods sold under control.
### Step-by-step Analysis:
1. Calculate Total Amount Spent on Materials:
- Material Purchased: 21,500 pounds
- Actual Cost per Pound: [tex]$3.25 \[ \text{Total Material Cost} = \text{Material Purchased} \times \text{Actual Cost per Pound} \] \[ \text{Total Material Cost} = 21,500 \times 3.25 = \$[/tex]69,875
\]
2. Calculate Standard Material Cost for Actual Production:
- Pools Produced: 5,000
- Standard Material Pounds per Pool: 3.3
- Standard Cost per Pound: [tex]$2.80 \[ \text{Standard Total Material Pounds} = \text{Pools Produced} \times \text{Standard Material Pounds per Pool} \] \[ \text{Standard Total Material Pounds} = 5,000 \times 3.3 = 16,500 \, \text{pounds} \] \[ \text{Standard Total Material Cost} = \text{Standard Total Material Pounds} \times \text{Standard Cost per Pound} \] \[ \text{Standard Total Material Cost} = 16,500 \times 2.80 = \$[/tex]46,200
\]
3. Calculate Material Price Variance:
- Actual Material Used: 16,300 pounds
- Actual Cost per Pound: [tex]$3.25 - Standard Cost per Pound: $[/tex]2.80
[tex]\[ \text{Material Price Variance} = (\text{Actual Cost per Pound} - \text{Standard Cost per Pound}) \times \text{Actual Material Used} \][/tex]
[tex]\[ \text{Material Price Variance} = (3.25 - 2.80) \times 16,300 = 0.45 \times 16,300 = \$7,335 \][/tex]
4. Calculate Material Quantity Variance:
- Actual Material Used: 16,300 pounds
- Standard Total Material Pounds for Production: 16,500 pounds
- Standard Cost per Pound: [tex]$2.80 \[ \text{Material Quantity Variance} = (\text{Actual Material Used} - \text{Standard Total Material Pounds}) \times \text{Standard Cost per Pound} \] \[ \text{Material Quantity Variance} = (16,300 - 16,500) \times 2.80 = -200 \times 2.80 = -\$[/tex]560
\]
5. Calculate Total Material Variance:
[tex]\[ \text{Total Material Variance} = \text{Material Price Variance} + \text{Material Quantity Variance} \][/tex]
[tex]\[ \text{Total Material Variance} = 7,335 + (-560) = \$6,775 \][/tex]
### Summary of Findings:
- Total Material Cost: [tex]$69,875 - Standard Total Material Cost: $[/tex]46,200
- Material Price Variance: [tex]$7,335 - Material Quantity Variance: -$[/tex]560
- Total Material Variance: $6,775
### Conclusion:
The direct materials' actual cost is significantly higher than the standard cost, primarily due to the price variance. This means that the primary issue is with the price being paid for the materials, which is higher than the standard expected rate. Additionally, there is a slight efficiency in the quantity of materials used, as seen in the negative quantity variance. Overall, Ms. Dunn should focus on negotiating better prices for materials to bring the variable cost of goods sold under control.
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