Math Problem Statement

An investment proposal will have annual fixed costs of $60,000, variable costs of $35 per unit of output, and revenue of $55 per unit of output. Determine the break-even quantity.

Solution

The problem asks for the break-even quantity, given the following details:

  • Annual fixed costs: $60,000
  • Variable costs per unit: $35
  • Revenue per unit: $55

Formula for Break-even Quantity:

Break-even quantity=Fixed CostsPrice per UnitVariable Cost per Unit\text{Break-even quantity} = \frac{\text{Fixed Costs}}{\text{Price per Unit} - \text{Variable Cost per Unit}}

Substituting the values:

Break-even quantity=60,0005535=60,00020=3,000 units\text{Break-even quantity} = \frac{60,000}{55 - 35} = \frac{60,000}{20} = 3,000 \text{ units}

So, the correct answer should be 3,000 units, not 300 units.

Would you like more details or have any questions?

Here are some additional questions:

  1. How does changing the fixed costs affect the break-even point?
  2. What happens to the break-even point if the variable cost per unit increases?
  3. How do you calculate profit after reaching the break-even quantity?
  4. What is the relationship between price per unit and break-even quantity?
  5. How could you reduce the break-even quantity?

Tip: The break-even analysis helps in understanding how costs and pricing impact your business's ability to cover its expenses.

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Math Problem Analysis

Mathematical Concepts

Break-even Analysis
Algebra

Formulas

Break-even quantity = Fixed Costs / (Price per Unit - Variable Cost per Unit)

Theorems

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Suitable Grade Level

Grades 10-12