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The problem in the image seems to describe a scenario involving a brick-making factory and a quadratic function related to the production of bricks. The function \( f(t) = -20t^2 + 240t - 1000 \) appears to model the production of bricks over time \( t \) (where \( t \) is likely in hours or another time unit). The problem then asks questions related to maximizing production, determining the time when maximum production occurs, and possibly other details related to production quantities.

Let's break down the problem and solve it step by step.

### 1. **Identify the function and its components:**
   \[
   f(t) = -20t^2 + 240t - 1000
   \]
   This is a quadratic function, where:
   - The coefficient of \( t^2 \) is negative (\( -20 \)), indicating the parabola opens downwards.
   - The function models the number of bricks produced over time \( t \).

### 2. **Find the time \( t \) at which production is maximized:**
   The maximum point of a downward-opening parabola occurs at the vertex. For a quadratic function in the form \( f(t) = at^2 + bt + c \), the time \( t \) at which the maximum occurs is given by:
   \[
   t = -\frac{b}{2a}
   \]
   Substituting the values from the function:
   \[
   t = -\frac{240}{2(-20)} = \frac{240}{40} = 6
   \]
   So, the maximum production occurs at \( t = 6 \) hours.

### 3. **Calculate the maximum number of bricks produced:**
   Substitute \( t = 6 \) back into the function to find the maximum production:
   \[
   f(6) = -20(6)^2 + 240(6) - 1000
   \]
   Calculate:
   \[
   f(6) = -20(36) + 1440 - 1000 = -720 + 1440 - 1000 = 720 - 1000 = -280
   \]
   However, this result seems unusual, suggesting perhaps a mistake in reading or interpreting the coefficients correctly, or there could be additional context needed from the problem. Typically, the production should be a positive number.

### 4. **Interpret the negative result:**
   The negative value could suggest something went wrong, like a misinterpretation of time intervals, or possibly an error in the context given. Normally, production should be positive, so there may be more instructions or context related to different intervals of time or other conditions.

### 5. **Other possible details:**
   The problem might ask about conditions before or after the maximum production, or about other specific times (e.g., when production starts, stops, or equals a certain value). These would be analyzed by solving the quadratic equation or evaluating the function at different time points.

Would you like further details on interpreting this, or solving other specific parts of the problem?

Here are some related questions you might consider:
1. What are the roots of the quadratic function (i.e., when does production start and end)?
2. How does the function behave before and after the time \( t = 6 \)?
3. What happens if the time \( t \) is extended beyond the maximum point?
4. How would you model this scenario if there were constraints on production time?
5. What other real-life factors might affect the production that aren't captured by this quadratic model?

**Tip:** In practical applications, always check the context and physical meaning behind mathematical results. If you get a negative value where a positive one is expected, it might indicate an issue with the model, an error in calculation, or a need to re-evaluate the problem's conditions.

Sebuah pabrik batu bata memiliki persamaan kuadratik untuk memodelkan produksi batu bata. Persamaan tersebut adalah f(t) = -20t^2 + 240t - 1000. Hitung waktu maksimum produksi dan banyaknya produksi maksimum.

Learn how to solve a brick production problem using the quadratic function f(t) = -20t^2 + 240t - 1000 to determine the maximum production time and the number of bricks produced. This solution covers key algebraic concepts and the vertex formula. Suitable for students in Grades 9-12.

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