To minimize the objective function $4x + 5y$ over a bounded feasible region, we follow these steps:

1. Identify the vertices of the feasible region: The minimum (or maximum) of a linear function over a polygonal region will occur at one of its vertices. These vertices are where the constraint lines intersect. Since you referred to a "displayed region," I would need the coordinates of the vertices of the region or a picture to analyze it further.

2. Evaluate the objective function at each vertex: Once the vertices are identified, we substitute the coordinates of each vertex into the objective function $4x + 5y$.

3. Compare the values: The vertex that gives the smallest value will provide the minimum value of $4x + 5y$.

If you can provide the vertices of the feasible region or a picture of the graph, I can proceed with calculating the minimum value.

Would you like to upload an image or provide the vertices of the region?

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Relative Questions:

1. What are the coordinates of the vertices of the feasible region?
2. What are the constraints that define this feasible region?
3. Have you already calculated the intersection points of the constraints?
4. Is this problem part of a specific linear programming example?
5. Would you like assistance in plotting the constraints to find the region?

Tip: Always ensure to identify the intersection points of constraints when solving linear programming problems graphically, as the optimal solution is located at one of these vertices.