1. **Problem statement:** Calculate various prices and profits related to selling cartons of strawberries with markup, markdown, and operating expenses. 2. **Formulas and rules:** - Selling price with markup: $$\text{Selling Price} = \text{Cost Price} \times (1 + \text{Markup Percentage})$$ - Breakeven price including operating expenses: $$\text{Breakeven Price} = \frac{\text{Cost Price}}{1 - \text{Operating Expense Percentage}}$$ - Markdown price: $$\text{Markdown Price} = \text{Original Selling Price} \times (1 - \text{Markdown Percentage})$$ - Profit or loss per carton: $$\text{Profit/Loss} = \text{Selling Price} - \text{Cost Price}$$ - Maximum markdown without loss: solve $$\text{Markdown Price} = \text{Breakeven Price}$$ for markdown percentage. 3. **Given data:** - Cost price per carton = 12 - Markup = 25% = 0.25 - Operating expenses = 15% = 0.15 - Markdown on unsold cartons = 20% = 0.20 4. **Step 1: Calculate selling price per carton with 25% markup** $$\text{Selling Price} = 12 \times (1 + 0.25) = 12 \times 1.25 = 15$$ 5. **Step 2: Calculate breakeven price per carton to cover cost and operating expenses** $$\text{Breakeven Price} = \frac{12}{1 - 0.15} = \frac{12}{0.85} \approx 14.12$$ 6. **Step 3: Calculate new selling price per carton with 20% markdown on original selling price** $$\text{Markdown Price} = 15 \times (1 - 0.20) = 15 \times 0.80 = 12$$ 7. **Step 4: Calculate profit or loss per carton on unsold cartons sold at markdown price** $$\text{Profit/Loss} = 12 - 12 = 0$$ So, there is no profit or loss; it breaks even. 8. **Step 5: Calculate maximum markdown percentage without incurring loss** Set markdown price equal to breakeven price: $$15 \times (1 - x) = 14.12$$ Solve for $$x$$: $$1 - x = \frac{14.12}{15} = 0.9413$$ $$x = 1 - 0.9413 = 0.0587 = 5.87\%$$ **Final answers:** - Selling price with 25% markup: 15 - Breakeven price: approximately 14.12 - Markdown price at 20% markdown: 12 - Profit/loss at markdown price: 0 (break even) - Maximum markdown without loss: approximately 5.87%