Final answer:
The question involves calculating total costs, operating income, and the contribution margin percentage for different cases based on the relationships between variable costs, fixed costs, and revenues.
Step-by-step explanation:
The question pertains to the calculation of total costs, operating income, and the contribution margin percentage in various business scenarios. Total costs are calculated by summing variable and fixed costs. Operating income is found by subtracting total costs from revenues. The contribution margin percentage is the contribution margin (revenues minus variable costs) divided by revenues, expressed as a percentage.
To solve for the missing values, we use these relationships:
- Total costs = Variable costs + Fixed costs.
- Operating Income = Revenues - Total costs.
- Contribution Margin = Revenues - Variable costs.
- Contribution Margin Percentage = (Contribution Margin / Revenues) × 100.
Let's calculate the missing values.
- Case a.
Total Costs = Variable Costs + Fixed Costs = $700 + $1,900 = $2,600.
Operating Income = Revenues - Total Costs = $400 - $2,600 = -$2,200 (a loss).
Contribution Margin Percentage = (($400 - $700) / $400) × 100 = -75%. - Case b.
Total Costs is given as $1,100.
Operating Income = Revenues - Total Costs = $2,700 - $1,100 = $1,600.
Contribution Margin Percentage = (($2,700 - $300) / $2,700) × 100 = 89%. - Case c.
Total Costs = Variable Costs + Fixed Costs = $500 + $800 = $1,300.
Operating Income = Revenues - Total Costs = $800 - $1,300 = -$500 (a loss).
Contribution Margin Percentage = (($800 - $500) / $800) × 100 = 38%. - Case d.
The Contribution Margin Percentage is given as 50%.
Contribution Margin = Revenues × Contribution Margin Percentage = $1,400 × 0.5 = $700.
Variable Costs = Revenues - Contribution Margin = $1,400 - $700 = $700.
Fixed Costs are not provided and cannot be calculated with given information; we assume it's the missing part of the equation.