A small business owner creates trivets from used wine corks...

A small business owner creates trivets from used wine corks and sells them over the Internet. The cost to make each trivet is $\$ 3$. She wants to pay herself a salary of $\$ 400$ a week. She sells each trivet for $\$ 18$ plus shipping. Find the number of trivets she needs to make and sell each week to break even. Round up to the nearest whole number.

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Key Concepts

Break-Even Analysis

Break-even analysis is a financial assessment used to determine the number of units that must be sold so that total revenues equal total costs, meaning there is no profit or loss. This analysis involves understanding both fixed and variable costs related to production and sales.

Fixed and Variable Costs

Fixed costs are expenses that remain constant regardless of the production volume, such as a consistent weekly salary. Variable costs, on the other hand, change directly with the number of units produced, such as the cost of materials per item. Recognizing these cost types is essential for understanding overall expense structures in business.

Unit Contribution Margin

The unit contribution margin is the amount by which the selling price per unit exceeds the variable cost per unit. This margin is crucial for determining how many units need to be sold to cover fixed costs, as it shows how much each unit contributes to overall profitability.

Rounding Considerations

When calculating the number of units needed to break even, it is important to round up to the nearest whole number since production and sales are typically quantified in full units. This guarantees that the costs are fully covered, avoiding any shortfall.

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