How to Complete the Corner Point Table

Oct 13, 2025 by miodeya.com 73 views

**Complete the Corner Point Table: A Guide to Solving Linear Programming Problems**

What is Linear Programming?

Linear programming is a method to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships. It is a way to find the optimal solution to a problem that involves maximizing or minimizing a linear objective function, subject to a set of linear constraints.

What is a Corner Point in Linear Programming?

In linear programming, a corner point is a point in the feasible region where the objective function has a maximum or minimum value. The feasible region is the set of all possible solutions to the linear programming problem, and the corner points are the vertices of this region.

How to Complete the Corner Point Table

To complete the corner point table, we need to find the values of the objective function at each of the corner points. The objective function is given by the equation C = 7x + 5y.

Step 1: Find the Corner Points

The corner points are the points where the constraints intersect. In this case, we have three constraints:

x = 0
y = 0
x + y = 15

We can find the corner points by solving these equations simultaneously.

Step 2: Evaluate the Objective Function at Each Corner Point

Once we have found the corner points, we need to evaluate the objective function at each point. We can do this by plugging in the values of x and y into the equation C = 7x + 5y.

Corner Point Table

Corner Point	x	y	C = 7x + 5y
(0,0)	0	0	0
(0,15)	0	15	75
(15,0)	15	0	105
(15,15)	15	15	180

Q&A

Q: What is the purpose of the corner point table in linear programming?

A: The corner point table is used to find the optimal solution to a linear programming problem. It helps us to identify the corner points of the feasible region, where the objective function has a maximum or minimum value.

Q: How do I find the corner points of the feasible region?

A: To find the corner points, you need to solve the constraints simultaneously. In this case, we have three constraints: x = 0, y = 0, and x + y = 15. We can find the corner points by solving these equations simultaneously.

Q: How do I evaluate the objective function at each corner point?

A: To evaluate the objective function, you need to plug in the values of x and y into the equation C = 7x + 5y.

Q: What is the significance of the corner point table in real-world applications?

A: The corner point table is used in a variety of real-world applications, including resource allocation, production planning, and investment analysis. It helps decision-makers to identify the optimal solution to a problem, subject to a set of constraints.

Q: Can I use the corner point table to solve non-linear programming problems?

A: No, the corner point table is used to solve linear programming problems. Non-linear programming problems require a different approach, such as the use of numerical methods or approximation techniques.

Q: How do I determine the optimal solution from the corner point table?

A: To determine the optimal solution, you need to identify the corner point with the maximum or minimum value of the objective function. In this case, the optimal solution is the corner point (15,15) with a value of C = 180.

Conclusion

In conclusion, the corner point table is a powerful tool in linear programming that helps us to find the optimal solution to a problem. By completing the corner point table, we can identify the corner points of the feasible region, evaluate the objective function at each point, and determine the optimal solution.