Break Even Analysis
1. **Stating the problem:** NWF wants to find the break-even point in units and total sales for a cedar picnic table that sells for 50 each, with fixed costs of 13000 and variable costs per table of 22.
2. **Define variables:** Let $x$ be the number of tables sold to break even.
3. **Break-even point condition:** Break-even occurs where total revenue equals total costs.
- Total revenue = price per table $\times x = 50x$
- Total cost = fixed cost + variable cost per table $\times x = 13000 + 22x$
4. **Set revenue equal to costs:**
$$50x = 13000 + 22x$$
5. **Solve for $x$:**
$$50x - 22x = 13000$$
$$28x = 13000$$
$$x = \frac{13000}{28} = 464.2857...$$
6. **Interpretation:** Since they can't sell a fraction of a table, they need to sell at least 465 tables to break even.
7. **Total sales needed to break even:**
$$\text{Total sales} = \text{price} \times \text{units} = 50 \times 465 = 23250$$
**Final answers:**
- Tables to break even: 465
- Total sales to break even: 23250