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The image you uploaded appears to show sections from an assignment on linear programming or optimization. Here's a breakdown of the tasks you need to complete based on what I see:

1. **Section 4: The Graph and Vertices**  
   - It asks you to graph the constraints (likely inequalities) using a tool like Desmos.
   - After graphing, identify the vertices (corner points) of the feasible region formed by those constraints.

2. **Section 5: Evaluating the Vertices and Objective Function**  
   - Once you have the vertices from Section 4, you need to substitute them into the objective function (defined in Section 2, but not visible in this image).
   - Evaluate the objective function at each vertex and record the totals.

3. **Section 6: Interpreting the Answer**  
   - Based on your calculations in Section 5, explain which vertex gives the optimal solution.
   - You are also asked to determine the profit at the optimal solution, implying that this is a maximization problem (profit maximization).

### How to proceed:
1. **Graph the constraints** using Desmos or another graphing tool.
2. **List the vertices** from the feasible region.
3. **Substitute** these vertices into your objective function (from Section 2).
4. **Identify the vertex** that gives the highest (or lowest, if minimizing) value of the objective function.
5. **State the profit** at the optimal solution.

Would you like me to guide you on how to solve this step-by-step? Or if you share the constraints and the objective function from Section 2, I can assist with the calculations.

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Here are 5 questions to help you think further:
1. What are the four constraints that you need to graph in Section 4?
2. Can you describe the objective function from Section 2?
3. How do you determine the vertices of a feasible region when graphing inequalities?
4. What is the relationship between vertices and finding optimal solutions in linear programming?
5. How will you verify that the optimal solution is correct?

**Tip**: When working with linear programming, always ensure that your feasible region is bounded; otherwise, there may not be an optimal solution.

The image uploaded by the user appears to show sections from an assignment on linear programming or optimization, focusing on graphing constraints, identifying vertices, evaluating objective functions, and interpreting results.

Explore how to solve a linear programming problem by graphing constraints, identifying vertices of the feasible region, and evaluating the objective function to find the optimal solution. Suitable for Grades 10-12 students.

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