Math Problem Statement
A firm manufactures a product that sells for $12 per unit. Variable cost per unit is $7 and fixed cost per period is $ 1800. Capacity per period is 800 units. Perform a break-even analysis showing a detailed break-even chart.
Solution
Here is the break-even chart based on the information provided:
- The Total Revenue line starts from the origin with a slope of $12 (revenue per unit).
- The Total Cost line starts at $1,800 (the fixed cost) and increases by $7 per unit.
- The break-even point occurs at 360 units and $4,320 in revenue, where the two lines intersect.
Would you like further details or clarification?
Relative Questions:
- How would changes in variable costs impact the break-even point?
- What happens to the break-even point if fixed costs increase by 10%?
- How is profit calculated beyond the break-even point?
- If the selling price decreases to $10 per unit, what is the new break-even point?
- How do economies of scale affect the break-even analysis?
Tip:
To lower the break-even point, you can reduce fixed costs, increase the selling price, or reduce variable costs.
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Math Problem Analysis
Mathematical Concepts
Break-even Analysis
Linear Equations
Revenue and Cost Functions
Formulas
Break-even Point (Units) = Fixed Costs / (Selling Price - Variable Cost)
Total Revenue = Selling Price × Quantity
Total Cost = Fixed Costs + (Variable Cost × Quantity)
Theorems
Break-even Theorem
Suitable Grade Level
Grades 10-12
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