Answer :
Alright, let's walk through the problem step-by-step to correctly solve each part.
### 1. Compute the Contribution Margin per Unit:
The contribution margin per unit is calculated by subtracting the variable cost per unit from the selling price per unit.
[tex]\[ \text{Contribution Margin per Unit} = \text{Selling Price per Unit} - \text{Variable Cost per Unit} \][/tex]
Given:
- Selling Price per Unit = \[tex]$360.00 - Variable Cost per Unit = \$[/tex]262.80
Therefore:
[tex]\[ \text{Contribution Margin per Unit} = 360.00 - 262.80 = 97.20 \][/tex]
So, the contribution margin per unit is \[tex]$97.20. ### 2. Compute the Contribution Margin Ratio: The contribution margin ratio is calculated by dividing the contribution margin per unit by the selling price per unit. \[ \text{Contribution Margin Ratio} = \frac{\text{Contribution Margin per Unit}}{\text{Selling Price per Unit}} \] Given: - Contribution Margin per Unit = \$[/tex]97.20
- Selling Price per Unit = \[tex]$360.00 Therefore: \[ \text{Contribution Margin Ratio} = \frac{97.20}{360.00} = 0.27 \] So, the contribution margin ratio is 0.27. ### 3. Compute Income if 5,700 Units are Produced and Sold: To compute the income, we need to calculate the total contribution margin and then subtract the fixed costs. First, calculate the total contribution margin: \[ \text{Total Contribution Margin} = \text{Contribution Margin per Unit} \times \text{Units Produced and Sold} \] Given: - Contribution Margin per Unit = \$[/tex]97.20
- Units Produced and Sold = 5,700
Therefore:
[tex]\[ \text{Total Contribution Margin} = 97.20 \times 5700 = 554,040.00 \][/tex]
Next, subtract the fixed costs to find the income:
[tex]\[ \text{Income} = \text{Total Contribution Margin} - \text{Fixed Costs} \][/tex]
Given:
- Total Contribution Margin = \[tex]$554,040.00 - Fixed Costs = \$[/tex]63,500.00
Therefore:
[tex]\[ \text{Income} = 554,040.00 - 63,500.00 = 490,540.00 \][/tex]
So, the income if 5,700 units are produced and sold is \[tex]$490,540.00. ### Summary of Results 1. Contribution Margin per Unit: \$[/tex]97.20
2. Contribution Margin Ratio: 0.27
3. Income if 5,700 units are produced and sold: \$490,540.00
(Note: The initial income reported in the question was 491,140, but the correct value is 490,540.00. This discrepancy suggests either a computational or typographical error in the initial solution.)
### 1. Compute the Contribution Margin per Unit:
The contribution margin per unit is calculated by subtracting the variable cost per unit from the selling price per unit.
[tex]\[ \text{Contribution Margin per Unit} = \text{Selling Price per Unit} - \text{Variable Cost per Unit} \][/tex]
Given:
- Selling Price per Unit = \[tex]$360.00 - Variable Cost per Unit = \$[/tex]262.80
Therefore:
[tex]\[ \text{Contribution Margin per Unit} = 360.00 - 262.80 = 97.20 \][/tex]
So, the contribution margin per unit is \[tex]$97.20. ### 2. Compute the Contribution Margin Ratio: The contribution margin ratio is calculated by dividing the contribution margin per unit by the selling price per unit. \[ \text{Contribution Margin Ratio} = \frac{\text{Contribution Margin per Unit}}{\text{Selling Price per Unit}} \] Given: - Contribution Margin per Unit = \$[/tex]97.20
- Selling Price per Unit = \[tex]$360.00 Therefore: \[ \text{Contribution Margin Ratio} = \frac{97.20}{360.00} = 0.27 \] So, the contribution margin ratio is 0.27. ### 3. Compute Income if 5,700 Units are Produced and Sold: To compute the income, we need to calculate the total contribution margin and then subtract the fixed costs. First, calculate the total contribution margin: \[ \text{Total Contribution Margin} = \text{Contribution Margin per Unit} \times \text{Units Produced and Sold} \] Given: - Contribution Margin per Unit = \$[/tex]97.20
- Units Produced and Sold = 5,700
Therefore:
[tex]\[ \text{Total Contribution Margin} = 97.20 \times 5700 = 554,040.00 \][/tex]
Next, subtract the fixed costs to find the income:
[tex]\[ \text{Income} = \text{Total Contribution Margin} - \text{Fixed Costs} \][/tex]
Given:
- Total Contribution Margin = \[tex]$554,040.00 - Fixed Costs = \$[/tex]63,500.00
Therefore:
[tex]\[ \text{Income} = 554,040.00 - 63,500.00 = 490,540.00 \][/tex]
So, the income if 5,700 units are produced and sold is \[tex]$490,540.00. ### Summary of Results 1. Contribution Margin per Unit: \$[/tex]97.20
2. Contribution Margin Ratio: 0.27
3. Income if 5,700 units are produced and sold: \$490,540.00
(Note: The initial income reported in the question was 491,140, but the correct value is 490,540.00. This discrepancy suggests either a computational or typographical error in the initial solution.)
