Question
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If the fixed costs are \( \$ 8,000 \) and variable costs are \( \$ 50 \) per item, what must the selling price be to break even on the manufacture of 500 items?

Ask by Salinas Estrada. in the United States
Jan 22,2025

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Answer

The selling price per item must be $66 to break even on the manufacture of 500 items.

Solution

To break even on the manufacture of 500 items, the total revenue from selling the items must equal the total cost of manufacturing the items. Let's denote the selling price per item as \( x \). The total revenue from selling 500 items is given by: \[ 500x \] The total cost of manufacturing 500 items is given by: \[ 500 \times 50 + 8000 \] To break even, the total revenue must equal the total cost: \[ 500x = 500 \times 50 + 8000 \] Now, we can solve for \( x \) to find the selling price per item. Solve the equation by following steps: - step0: Solve for \(x\): \(500x=500\times 50+8000\) - step1: Simplify: \(500x=33000\) - step2: Divide both sides: \(\frac{500x}{500}=\frac{33000}{500}\) - step3: Divide the numbers: \(x=66\) The selling price per item must be $66 to break even on the manufacture of 500 items.

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The Deep Dive

To break even on the manufacture of 500 items, you need to cover both your fixed and variable costs. Fixed costs are \$8,000, and the variable costs for 500 items amount to \( 500 \times 50 = \$25,000 \). So, the total costs are \( 8,000 + 25,000 = \$33,000 \). Dividing this total by the number of items gives you the selling price: \( \frac{33,000}{500} = \$66 \). Thus, the selling price must be \$66 per item to break even. To take it a step further, understanding contribution margin can also enhance your pricing strategy. Contribution margin is the difference between selling price and variable costs per item. In this case, if you sell each item for \$66, your contribution margin is \( 66 - 50 = 16 \). This margin not only helps cover fixed costs but also informs how much you can afford to reduce price or invest back into production.

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