1. **State the problem:** We need to find the cereal box dimensions that maximize the volume-to-surface-area ratio while meeting the constraints: - Volume between 3400 cm³ and 3425 cm³ - Height between 25 cm and 27 cm - Length between 18 cm and 20 cm - Width between 6 cm and 8 cm 2. **Analyze the given data:** The table provides height, length, width, volume, surface area, and volume-to-surface-area ratio for various box configurations. 3. **Calculate volume-to-surface-area ratio for each box:** The ratio is given as volume divided by surface area. We round each ratio to two decimal places: - For 25.5, 20.0, 6.6: $\frac{3366}{1621} \approx 2.08$ - For 27.0, 19.0, 6.7: $\frac{3437}{1642} \approx 2.09$ - For 26.5, 19.0, 6.8: $\frac{3424}{1626} \approx 2.11$ - For 26.0, 19.0, 6.9: $\frac{3409}{1609} \approx 2.12$ - For 25.5, 19.0, 7.0: $\frac{3392}{1592} \approx 2.13$ - For 27.0, 18.0, 7.1: $\frac{3451}{1611} \approx 2.14$ - For 26.5, 18.0, 7.2: $\frac{3434}{1595} \approx 2.15$ - For 26.0, 18.0, 7.3: $\frac{3416}{1578} \approx 2.16$ - For 25.5, 18.0, 7.4: $\frac{3397}{1562} \approx 2.17$ 4. **Check volume constraints:** The volume must be between 3400 and 3425 cm³. - Only the boxes with volumes 3424, 3409, 3416, and 3397 cm³ are close to or within this range. - 3397 is slightly below 3400, so exclude it. 5. **Compare ratios for valid volumes:** Among 3424, 3409, and 3416: - 3424 cm³ box ratio: 2.11 - 3409 cm³ box ratio: 2.12 - 3416 cm³ box ratio: 2.16 6. **Select the best box:** The box with dimensions height = 26.0 cm, length = 18.0 cm, width = 7.3 cm has volume 3416 cm³ and the highest volume-to-surface-area ratio of approximately 2.16, meeting all constraints. **Final answer:** The best cereal box size is height 26.0 cm, length 18.0 cm, width 7.3 cm, with volume 3416 cm³ and surface area 1578 cm², maximizing the volume-to-surface-area ratio at approximately 2.16.