This worksheet is asking you to evaluate the graph and vertices, objective function, and interpret your solution based on the problem you're working on. Let me guide you through the sections:

Section 4: The Graph and Vertices

• Task: You're required to use Desmos (or any graphing tool) to graph the four constraints you've defined in Section 3. Once you create the feasible region (where all the inequalities overlap), you need to record the vertices of that feasible region in the table provided.

Section 5: Evaluating the Vertices and Objective Function

• Task: After identifying the vertices, you need to use the objective function from Section 2 and plug in the values of each vertex to calculate the result (objective value). You will fill in the table for each vertex with:
  • The vertex (coordinates),
  • The calculated objective function value,
  • The total or result for each vertex.

Section 6: Interpreting the Answer

• Task: Based on the objective function values you computed in Section 5, you need to find the vertex that gives you the optimal solution (either the maximum or minimum value, depending on the type of optimization problem—profit maximization or cost minimization, etc.).
• What is the optimal solution?: This will be the vertex that provides the best value for the objective function.
• What is the profit at the optimal solution?: You need to determine the objective function value at the optimal vertex.

Next Steps:

1. Do you already have the constraints and the objective function to begin graphing?
2. Have you plotted the feasible region using Desmos or a graphing tool yet?
3. If you'd like, I can assist with solving the objective function for the vertices once you provide them.
4. Would you like to discuss how to solve these problems step by step?
5. Do you need assistance in understanding how to use the objective function?

Tip: Always double-check your constraints and graph, as small mistakes in defining the region can lead to incorrect vertices and suboptimal solutions.