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The image you uploaded is a mathematical problem involving operations of two silos (S1 and S2) for maize storage and extraction, focusing on national and export markets. The mathematical modeling includes differential equations and time-dependent rates of extraction, with different scenarios for each silo. Here’s a breakdown of the key parts:

### General Setup:
1. **Extraction Equations for Silos**:
   - The extraction for **Silo 1 (S₁)** is modeled by the function:
     \[
     S_1(t) = -5t + 220
     \]
   - The extraction for **Silo 2 (S₂)** (for export) follows:
     \[
     S_2(t) = -0.8t + 540
     \]

These equations describe how the amount of maize decreases with time \(t\) (in hours).

### Silo 1 (S₁) - National Market:
This silo serves the national market, and the first part of the problem asks the following questions:
1. **How many tons of maize are there at the beginning of the 32-hour extraction operation?**
   - Use \(t = 0\) in \(S_1(t)\) to find the initial tons.
2. **After how many hours since the start of the operation will the silo be empty?**
   - Solve \(S_1(t) = 0\) to find \(t\).
3. **How many tons remain after a certain amount of hours?**
   - Plug in the given time into \(S_1(t)\).

### Silo 2 (S₂) - Export Market:
This silo serves export purposes. The problem for this silo is similar to S₁ but with different parameters:
1. **Initial amount of maize and the duration of the extraction.**
   - Use \(S_2(t)\) to find out how long it takes for the silo to empty and how much maize is there at different times.
2. **Duration to empty the silo** and **remaining maize after certain hours** are key questions for S₂ as well.

### Comparison and Analysis:
The problem also includes a comparative analysis of the two silos, asking for the amount of maize in each after a certain number of hours and identifying the silo with the largest amount of maize remaining.

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To resolve this, the main approach is:
1. Substitute values of \(t\) in the given functions \(S_1(t)\) and \(S_2(t)\) to find amounts of maize and solve for the time when the silo is empty (by setting the function equal to zero).
2. Compare the results for both silos over time.

Would you like me to proceed with solving the specific questions outlined in the image?

Operations involving the extraction of maize from two silos (S1 and S2) for national and export markets using differential equations.

This problem explores maize extraction operations from two silos using linear equations for both national and export markets. It includes calculating the initial quantity, the time required to empty the silos, and comparative analysis of remaining quantities over time. Suitable for students in Grades 10-12.

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