The Oliver Company plans to market a new product. Based on its market studies, Oliver estimates that it can sell up to 5,500 units in 2005. The selling price will be $5 per unit. Variable costs are estimated to be 30% of total revenue. Fixed costs are estimated to be $5,600 for 2005. How many units should the company sell to break even?
units

To find the break-even point, we need to determine how many units Oliver Company should sell so that total revenue equals total costs (fixed + variable costs).

### Definitions:
- **Selling Price (P):** $5 per unit
- **Variable Cost:** 30% of total revenue
- **Fixed Costs (F):** $5,600
- **Revenue (R):** $ R = P \times Q $ where $ Q $ is the number of units sold.

### Break-even point occurs when:
\[
\text{Total Revenue} = \text{Total Costs}
\]
\[
\text{Total Costs} = \text{Fixed Costs} + \text{Variable Costs}
\]
\[
\text{Variable Costs} = 30\% \times \text{Revenue}
\]

### Steps:

1. **Revenue:**
   \[
   \text{Revenue} = 5Q
   \]

2. **Variable Costs:**
   \[
   \text{Variable Costs} = 0.30 \times 5Q = 1.5Q
   \]

3. **Total Costs:**
   \[
   \text{Total Costs} = \text{Fixed Costs} + \text{Variable Costs} = 5600 + 1.5Q
   \]

4. **Break-even Point:**
   \[
   \text{Revenue} = \text{Total Costs}
   \]
   \[
   5Q = 5600 + 1.5Q
   \]

   Solving for $ Q $:

   \[
   5Q - 1.5Q = 5600
   \]
   \[
   3.5Q = 5600
   \]
   \[
   Q = \frac{5600}{3.5} = 1600
   \]

Thus, the company needs to sell **1,600 units** to break even.

Would you like further details or explanations? Here are 5 related questions to deepen your understanding:

1. What happens if the selling price increases or decreases?
2. How would changes in fixed costs affect the break-even point?
3. What is the total profit if 2,000 units are sold?
4. How can Oliver Company reduce its break-even point?
5. What is the contribution margin per unit?

**Tip:** The contribution margin is the amount per unit that contributes to covering fixed costs after variable costs have been paid.

The Oliver Company plans to market a new product. Based on its market studies, Oliver estimates that it can sell up to 5,500 units in 2005. The selling price will be $5 per unit. Variable costs are estimated to be 30% of total revenue. Fixed costs are estimated to be $5,600 for 2005. How many units should the company sell to break even?

Find out how many units Oliver Company needs to sell to break even in 2005. With a selling price of $5 per unit, 30% variable costs, and fixed costs of $5,600, this analysis walks through the step-by-step calculation to determine the break-even point at 1,600 units.

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