In a linear programming problem, which one of the following is correct...
Graphical method in Linear Programming
Feasible region
For a linear programming problem, the feasible region is the set of all feasible solutions that satisfy all the constraints of the problem. The feasible region is bounded by the boundary lines of the constraints and the non-negativity constraints.
Corner points and Optimum solution
Corner points are the intersection points of the boundary lines of the constraints. The optimum solution to the linear programming problem is one of the corner points of the feasible region.
Objective function
The objective function of a linear programming problem is the function that is to be optimized or minimized. The objective function is represented by a linear equation. The objective function lines are parallel to each other and their slope represents the objective coefficient.
Correct statement for graphical method
From the given options, option B is correct. One of the corner points of the feasible region may not be the optimum solution. This is because the objective function lines are parallel to each other, and the optimum solution may lie on any of these parallel lines. Thus, the optimum solution may not always be a corner point of the feasible region.
Conclusion
Graphical method is a useful tool for solving linear programming problems. It helps in visualizing the feasible region and identifying the optimum solution. However, it is important to note that the optimum solution may not always be a corner point of the feasible region.