1. **State the problem:** The Puzzle Company wants to find the total sales volume needed to achieve a net income of $1,000,000 given total revenue, fixed costs, and variable costs. 2. **Identify given values:** - Total revenue $R = 4,634,500$ - Fixed costs $F = 1,122,500$ - Variable costs $V = 2,010,500$ - Desired net income $I = 1,000,000$ 3. **Recall the formula for net income:** $$\text{Net Income} = \text{Total Revenue} - \text{Total Fixed Costs} - \text{Total Variable Costs}$$ 4. **Define sales volume:** Let $n$ be the break-even sales volume where net income is zero. At break-even, $$R = F + V$$ 5. **Calculate contribution margin per unit:** Contribution margin per unit $= \frac{R - V}{n}$ 6. **Express total sales volume $S$ needed to achieve net income $I$:** $$I = (S \times \text{contribution margin per unit}) - F$$ Rearranged, $$S = \frac{I + F}{\text{contribution margin per unit}}$$ 7. **Substitute contribution margin per unit:** $$S = \frac{I + F}{\frac{R - V}{n}} = n \times \frac{I + F}{R - V}$$ 8. **Plug in values:** $$S = n \times \frac{1,000,000 + 1,122,500}{4,634,500 - 2,010,500} = n \times \frac{2,122,500}{2,624,000} \approx n \times 0.8087$$ **Final answer:** The total sales volume needed to achieve a net income of 1,000,000 is approximately $$S \approx 0.8087 \times n$$ where $n$ is the break-even sales volume.