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The given problem refers to a cost function for producing toasters, denoted as $ C(n) = 200 - 10n + 10n^2 $, where $ n $ represents the number of toasters.

We are provided two key pieces of information:
1. The cost of producing 10 toasters is \$1000 (true statement).
2. The cost of producing 20 toasters is not \$4000 (false statement).

### Let's verify both claims:

1. **Check if the cost of producing 10 toasters is \$1000:**
   We substitute $ n = 10 $ into the cost function $ C(n) $:

   \[
   C(10) = 200 - 10(10) + 10(10^2)
   \]
   \[
   C(10) = 200 - 100 + 10(100)
   \]
   \[
   C(10) = 200 - 100 + 1000 = 1100
   \]

   The actual cost of producing 10 toasters is \$1100, not \$1000. Therefore, the statement is false.

2. **Check if the cost of producing 20 toasters is \$4000:**
   We substitute $ n = 20 $ into the cost function $ C(n) $:

   \[
   C(20) = 200 - 10(20) + 10(20^2)
   \]
   \[
   C(20) = 200 - 200 + 10(400)
   \]
   \[
   C(20) = 200 - 200 + 4000 = 4000
   \]

   The actual cost of producing 20 toasters is \$4000, which matches the given false claim. Thus, the second statement is false.

### Conclusion:
Both statements provided in the problem are false. The correct cost for producing 10 toasters is \$1100, and the cost for 20 toasters is indeed \$4000.

Would you like more details on the steps taken? Here are five related questions to deepen your understanding:

1. How do quadratic functions like this cost function behave in terms of increasing or decreasing costs?
2. How could you determine the number of toasters where production cost is minimized?
3. What is the significance of the negative linear term in the cost function?
4. How would you calculate the marginal cost from this cost function?
5. How could the cost function be adjusted to match the given true or false cost scenarios?

**Tip**: Always check your results by substituting values directly into the function, ensuring accuracy in problem-solving.

Es verdad que el costo de producir '10' tostadoras en dólares, es 1000 y es falso que el costo de producir '20' tostadoras en dólares es 4000, en la siguiente función de producción: C(n) = 200 - 10n + 10n^2.

Learn how to verify the cost of producing 10 and 20 toasters using the quadratic function C(n) = 200 - 10n + 10n^2. Analyze whether the cost for producing 10 toasters is $1000 and if the cost for 20 toasters is $4000. Suitable for Grades 10-12.

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