📚 Topic Summary
In Algebra 2, identifying feasible region vertices is a key skill in linear programming. The feasible region is the set of all possible solutions to a system of linear inequalities. Vertices are the corner points of this region, formed by the intersection of the boundary lines. These vertices are crucial because the optimal solution (maximum or minimum) of a linear objective function always occurs at one of these vertices. To find them, graph the inequalities, identify the feasible region, and then determine the coordinates of the corner points.
Understanding feasible region vertices allows us to solve real-world optimization problems, such as maximizing profit or minimizing cost, subject to various constraints. By evaluating the objective function at each vertex, we can determine the optimal solution within the given constraints.
🧮 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Feasible Region |
A. A function to be maximized or minimized. |
| 2. Vertex |
B. The corner point of the feasible region. |
| 3. Objective Function |
C. A line that defines the boundary of the feasible region. |
| 4. Constraint |
D. The set of all possible solutions to a system of inequalities. |
| 5. Boundary Line |
E. A limitation or restriction expressed as an inequality. |
Match the letters with the numbers above.
✍️ Part B: Fill in the Blanks
The feasible region is the set of all possible _________ to a system of linear _________. Vertices are the _________ points of this region, formed by the intersection of the _________ lines. The optimal solution of a linear objective function always occurs at one of these _________.
🤔 Part C: Critical Thinking
Explain, in your own words, why identifying the vertices of a feasible region is important in solving optimization problems. Provide a real-world example where this concept might be applied.