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The problem on your screen is asking to form a system of linear inequalities that represents a furniture manufacturing scenario.

### Given Information:
- **Tables** require:
  - 11 labor-hours for assembly.
  - 4 labor-hours for finishing.
- **Chairs** require:
  - 8 labor-hours for assembly.
  - 3 labor-hours for finishing.
- **Constraints**:
  - Maximum labor hours available per day for **assembly**: 425.
  - Maximum labor hours available per day for **finishing**: 130.

We need to define:
- Let \( x \) be the number of tables.
- Let \( y \) be the number of chairs.

### Step-by-Step Setup:
1. **Assembly constraint**:
   - The total labor for assembling tables is \( 11x \) (since each table takes 11 hours).
   - The total labor for assembling chairs is \( 8y \) (since each chair takes 8 hours).
   - Together, the total labor for assembly cannot exceed 425 hours:
     \[
     11x + 8y \leq 425
     \]

2. **Finishing constraint**:
   - The total labor for finishing tables is \( 4x \) (since each table takes 4 hours).
   - The total labor for finishing chairs is \( 3y \) (since each chair takes 3 hours).
   - Together, the total labor for finishing cannot exceed 130 hours:
     \[
     4x + 3y \leq 130
     \]

### System of Inequalities:
- For assembly: \( 11x + 8y \leq 425 \)
- For finishing: \( 4x + 3y \leq 130 \)

These inequalities represent the limits on labor hours for manufacturing tables and chairs in a day.

Would you like further explanation on any part? Let me know if you need details or have any questions!

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Here are 5 follow-up questions to deepen your understanding:

1. How would the system change if the labor-hour limits for assembly or finishing were increased or decreased?
2. What does the solution of the system represent in terms of how many tables and chairs can be manufactured in a day?
3. How could you solve this system of inequalities graphically?
4. What would happen if you introduced another product, like benches, with different labor-hour requirements?
5. Can the system be solved using linear programming to maximize profit if the prices of tables and chairs are known?

**Tip**: When dealing with systems of inequalities, plotting the constraints can help visualize the feasible region of solutions.

A furniture manufacturing company produces tables and chairs. Tables require 11 labor-hours for assembly and 4 labor-hours for finishing. Chairs require 8 labor-hours for assembly and 3 labor-hours for finishing. The company has 425 labor-hours available per day for assembly and 130 for finishing. Write a system of inequalities for this situation using x for the number of tables and y for the number of chairs manufactured in a day.

Learn how to solve a system of linear inequalities for a furniture manufacturing scenario. This problem involves determining labor constraints for assembling and finishing tables and chairs. Suitable for students in Grades 9-12.

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