Math Problem Statement
Solution
To calculate the break-even point for the company as a whole, we first need to use the data provided in the table. Let's break down the process step by step:
Given Data:
For product F1:
- Selling price (LE): 50
- Variable cost per unit (LE): 30
- Fixed cost for product (LE): 2000
- Expected sales volume: 500
For product F2:
- Selling price (LE): 36
- Variable cost per unit (LE): 27
- Fixed cost for product (LE): 6000
- Expected sales volume: 2000
Step 1: Contribution margin per unit for each product
The contribution margin is calculated as:
For F1:
For F2:
Step 2: Total fixed costs
Total fixed costs are the sum of the fixed costs for both products:
Step 3: Sales mix (proportion of each product's sales)
Sales mix is the proportion of sales volume of each product to the total sales volume.
Step 4: Weighted average contribution margin
The weighted average contribution margin (WACM) is calculated as the sum of the contribution margins of both products, weighted by their sales mix:
Step 5: Break-even point (in units)
The break-even point in units can be calculated using the formula:
Step 6: Break-even point (in sales volume)
Now, to find the break-even point in terms of sales for each product, we distribute the 714.29 units based on the sales mix:
- For F1:
- For F2:
Thus, the company must sell approximately 143 units of F1 and 571 units of F2 to break even.
Would you like a further explanation of any step or additional details?
Here are 5 related questions you might find useful:
- How does changing the fixed cost impact the break-even point?
- How would changes in the sales mix affect the weighted average contribution margin?
- What is the break-even point in terms of revenue instead of units?
- How can this analysis be adapted for more than two products?
- What role does the contribution margin play in determining profitability?
Tip: Always consider the sales mix when calculating the break-even point for multiple products—it can significantly impact the overall result.
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Math Problem Analysis
Mathematical Concepts
Break-even analysis
Cost accounting
Profit planning
Formulas
Contribution Margin = Selling Price - Variable Cost
Total Fixed Costs = Fixed Costs for F1 + Fixed Costs for F2
Weighted Average Contribution Margin = (Sales Mix F1 * Contribution Margin F1) + (Sales Mix F2 * Contribution Margin F2)
Break-even Point (Units) = Total Fixed Costs / Weighted Average Contribution Margin
Theorems
Break-even point theory
Suitable Grade Level
Grades 10-12 (Business and Economics)
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