1. **Problem statement:** A greeting cards company sells cards for 3 each. The total cost is 3000 fixed plus 1 per card variable cost. 2. **Break-even point:** Break-even means total revenue equals total cost. 3. **Formulas:** - Total revenue $R = 3x$ where $x$ is number of cards sold. - Total cost $C = 3000 + 1x$ 4. **Set revenue equal to cost:** $$3x = 3000 + 1x$$ 5. **Solve for $x$:** $$3x - 1x = 3000$$ $$2x = 3000$$ $$x = \frac{3000}{2}$$ $$x = 1500$$ 6. **Interpretation:** The company must sell 1500 cards to break even. --- 7. **Average cost function:** Average cost $AC = \frac{\text{Total cost}}{\text{Number of units}} = \frac{3000 + x}{x}$ 8. **Simplify average cost:** $$AC = \frac{3000}{x} + \frac{x}{x} = \frac{3000}{x} + 1$$ 9. **Calculate average cost for 1500 units:** $$AC = \frac{3000}{1500} + 1 = 2 + 1 = 3$$ 10. **Interpretation:** The average cost of producing 1500 cards is 3 each.