Question
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If fixed costs to print a certain Bible are \( \$ 15,000 \) and variable costs are \( \$ 25 \) per Bible, what must be the selling price to earn \( \$ 10 \) per Bible if 5,000 Bibles are printed?

Ask by Moreno Robbins. in the United States
Jan 22,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

To earn \$10 per Bible, you should sell each Bible for \$38.

Solution

To determine the selling price per Bible that allows you to earn a profit of \$10 per Bible when printing 5,000 Bibles, follow these steps: 1. **Calculate Total Fixed Costs:** \[ \text{Fixed Costs} = \$15,000 \] 2. **Calculate Total Variable Costs:** \[ \text{Variable Cost per Bible} = \$25 \\ \text{Total Variable Costs} = \$25 \times 5,000 = \$125,000 \] 3. **Determine Total Cost:** \[ \text{Total Cost} = \text{Fixed Costs} + \text{Total Variable Costs} = \$15,000 + \$125,000 = \$140,000 \] 4. **Calculate Desired Total Profit:** \[ \text{Desired Profit per Bible} = \$10 \\ \text{Total Desired Profit} = \$10 \times 5,000 = \$50,000 \] 5. **Determine Required Total Revenue:** \[ \text{Total Revenue} = \text{Total Cost} + \text{Total Desired Profit} = \$140,000 + \$50,000 = \$190,000 \] 6. **Find the Selling Price per Bible:** \[ \text{Selling Price per Bible} = \frac{\text{Total Revenue}}{\text{Number of Bibles}} = \frac{\$190,000}{5,000} = \$38 \] **Conclusion:** You must set the selling price at **\$38 per Bible** to achieve a profit of \$10 per Bible when printing 5,000 Bibles.

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The Deep Dive

To determine the selling price to earn a profit of \( \$10 \) per Bible, you first need to calculate the total costs and the total number of Bibles. The fixed costs are \( \$15,000 \), and the variable costs for printing 5,000 Bibles at \( \$25 \) each amount to \( 5,000 \times 25 = \$125,000 \). Thus, the total cost is \( 15,000 + 125,000 = \$140,000 \). Now, to find the selling price that allows for a profit of \( \$10 \) per Bible, we first determine the total desired profit from selling 5,000 Bibles, which is \( 5,000 \times 10 = 50,000 \). Therefore, the overall revenue needed would be the total costs plus the desired profit: \( 140,000 + 50,000 = \$190,000 \). Finally, to find the selling price per Bible, divide the total revenue by the number of Bibles: \[ \text{Selling Price} = \frac{190,000}{5,000} = \$38. \] So, the selling price must be \( \$38 \) per Bible to earn \( \$10 \) profit on each one when 5,000 Bibles are printed.

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