1. **State the problem:** The cost of making one chair is 28 dollars, correct to the nearest dollar. We need to find the lower and upper limits for the total cost of making 450 chairs. 2. **Understanding the rounding:** Since the cost is rounded to the nearest dollar, the actual cost per chair could be as low as $27.5$ (just above 27.5 rounds up to 28) and as high as $28.5$ (just below 28.5 rounds down to 28). 3. **Calculate the lower limit for one chair:** $$\text{Lower limit} = 28 - 0.5 = 27.5$$ 4. **Calculate the upper limit for one chair:** $$\text{Upper limit} = 28 + 0.5 = 28.5$$ 5. **Calculate the lower limit for 450 chairs:** $$450 \times 27.5 = 12375$$ 6. **Calculate the upper limit for 450 chairs:** $$450 \times 28.5 = 12825$$ 7. **Final answer:** The lower limit for the total cost is $12375$ and the upper limit is $12825$ for making 450 chairs.