Widget World makes a widget that is sells for $10 per unit. The variable costs are $7 per unit. Assuming the business has normal fixed costs and the break-even point is 350 units, what are the total costs at break-even?

Question

BlackTom AI · Accepted Answer

Break-even occurs when total revenue equals total costs (fixed + variable), so revenue per unit times units equals fixed costs plus variable cost per unit times units.

1) Relevant knowledge points and concepts
- Break-even point in units: Fixed Costs / Contribution Margin per unit.
- Contribution margin per unit = Selling Price per unit − Variable Cost per unit.
- At break-even, Total Revenue = Total Costs. Total Revenue = Price × Units. Total Costs = Fixed Costs + (Variable Cost per unit × Units).

2) Complete reasoning process step by step
- Given: Price = $10 per unit; Variable cost = $7 per unit; Break-even units = 350.
- Compute contribution margin per unit:
  Contribution = $10 − $7 = $3 per unit.
- Use the break-even formula to infer Fixed Costs:
  Break-even units = Fixed Costs / Contribution → 350 = Fixed Costs / $3.
  Solve for Fixed Costs: Fixed Costs = 350 × $3 = $1,050.
- Compute total variable costs at break-even:
  Variable Costs total = Variable cost per unit × Units = $7 × 350 = $2,450.
- Compute total costs at break-even:
  Total Costs = Fixed Costs + Total Variable Costs = $1,050 + $2,450 = $3,500.
- Check via revenue equality:
  Total Revenue at break-even = Price × Units = $10 × 350 = $3,500, which matches Total Costs (consistency check).

3) Intermediate calculations shown
- Contribution per unit = 10 − 7 = 3
- Fixed Costs = 350 × 3 = 1,050
- Variable Costs total = 7 × 350 = 2,450
- Total Costs = 1,050 + 2,450 = 3,500
- Revenue = 10 × 350 = 3,500

4) Why the correct answer is correct
Because at break-even total revenue must equal total costs. Using the given price, variable cost, and break-even units yields fixed costs of $1,050 and total variable costs of $2,450; their sum is $3,500, which equals revenue at 350 units.

5) Why other possible answers would be incorrect
- $1,050 would represent fixed costs only, not total costs.
- $2,450 would represent total variable costs at 350 units, not total costs.
- Any number not equal to $3,500 would fail the condition Total Revenue = Total Costs at break-even.

Conclusion: The total costs at break-even are $3,500, which matches the provided correct answer $3500.

Widget World makes a widget that is sells for $10 per unit. The variable costs are $7 per unit. Assuming the business has normal fixed costs and the break-even point is 350 units, what are the total costs at break-even?单项选择题

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