1. **State the problem:** Jacques has a weekly budget of 24 to spend on candy bars and eggs. Candy bars cost 2 per pack, eggs cost 6 per dozen. We want to find how many packs or dozens he can buy if he spends all his money on one good, plot the budget constraint, and interpret the slope. 2. **Calculate maximum quantities:** - If Jacques spends all 24 on candy bars: $$\frac{24}{2} = 12$$ packs. - If Jacques spends all 24 on eggs: $$\frac{24}{6} = 4$$ dozens. 3. **Budget constraint equation:** Let $x$ = packs of candy bars, $y$ = dozens of eggs. The total spending must satisfy: $$2x + 6y = 24$$ 4. **Rewrite budget constraint for graphing:** Solve for $y$: $$6y = 24 - 2x$$ $$y = 4 - \frac{1}{3}x$$ This line has intercepts at $x=12$ (candy bars) and $y=4$ (eggs). 5. **Interpret slope:** The slope is $$-\frac{1}{3}$$ which means for each additional pack of candy bars, Jacques must give up $$\frac{1}{3}$$ dozen eggs. This represents the opportunity cost of an additional pack of candy bars in terms of dozens of eggs. 6. **Spending 12 on each good:** - Spending 12 on candy bars: $$\frac{12}{2} = 6$$ packs. - Spending 12 on eggs: $$\frac{12}{6} = 2$$ dozens. Point on budget line: $(6, 2)$. 7. **If Jacques receives an additional 24:** New budget = 24 + 24 = 48. New budget constraint: $$2x + 6y = 48$$ Intercepts: - Candy bars: $$\frac{48}{2} = 24$$ packs. - Eggs: $$\frac{48}{6} = 8$$ dozens. Slope remains $$-\frac{1}{3}$$. 8. **Tradeoff remains the same:** Since prices did not change, the slope (tradeoff rate) remains the same. **Final answers:** - Maximum candy bars: 12 packs. - Maximum eggs: 4 dozens. - Slope represents the opportunity cost of an additional pack of candy bars in terms of dozens of eggs. - Spending 12 on each good corresponds to point (6, 2). - New budget constraint intercepts: 24 candy bars, 8 eggs. - Tradeoff is the same (True).