Math Problem Statement

What is the company's total fixed cost amount?

Solution

To calculate the company's total fixed cost, we can use the break-even point formula:

Break-even point (units)=Fixed costsPrice per unitVariable cost per unit\text{Break-even point (units)} = \frac{\text{Fixed costs}}{\text{Price per unit} - \text{Variable cost per unit}}

Given:

  • Break-even point units = 17,500
  • Price per unit = $26.50
  • Variable cost per unit = $15.25

Let's rearrange the formula to solve for the fixed costs:

Fixed costs=Break-even point units×(Price per unitVariable cost per unit)\text{Fixed costs} = \text{Break-even point units} \times (\text{Price per unit} - \text{Variable cost per unit})

Substituting the values:

Fixed costs=17,500×(26.5015.25)=17,500×11.25=196,875\text{Fixed costs} = 17,500 \times (26.50 - 15.25) = 17,500 \times 11.25 = 196,875

So, the company's total fixed cost is $196,875.

Would you like more details or have any questions about this calculation?

Here are some related questions to further explore:

  1. How do variable costs impact the break-even point?
  2. What happens to the break-even point if the price per unit decreases?
  3. How do fixed costs differ from variable costs?
  4. How would a change in fixed costs affect profitability?
  5. Can break-even analysis be applied to service industries?

Tip: In break-even analysis, always differentiate between fixed and variable costs to determine the level of sales needed to cover all costs.

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Math Problem Analysis

Mathematical Concepts

Break-even analysis
Fixed costs
Variable costs

Formulas

Break-even point (units) = Fixed costs / (Price per unit - Variable cost per unit)
Fixed costs = Break-even point units × (Price per unit - Variable cost per unit)

Theorems

Break-even analysis

Suitable Grade Level

Grades 10-12