Linear Programming

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What is Linear Programming?

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Linear Programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model. Its function is to maximize or minimize a linear objective function, subject to linear equality and inequality constraints.

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What is an Objective Function in Linear Programming?

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An Objective Function is a mathematical expression that defines the goal of the linear programming problem, typically to maximize or minimize a certain quantity, such as profit or cost.

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What are feasible solutions in Linear Programming?

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Feasible solutions are the set of all possible points that satisfy the constraints of a linear programming problem. They are found within the feasible region.

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What is the feasible region in Linear Programming?

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The feasible region is the set of all feasible solutions that satisfy all constraints of a linear programming problem, often represented graphically as a polygon.

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What are corner points in Linear Programming?

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Corner points (or vertices) are the points at which the edges of the feasible region intersect. They are critical in linear programming as the optimal solution lies at one of these points.

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How do you determine the optimal solution in Linear Programming?

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The optimal solution is determined by evaluating the objective function at each corner point of the feasible region and selecting the point that yields the highest (or lowest) value, depending on the goal.

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What is the significance of constraints in Linear Programming?

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Constraints are the restrictions or limitations on the decision variables in a linear programming problem. They define the feasible region and ensure that the solutions are practical.

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What is a linear inequality?

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What does it mean for a solution to be bounded in Linear Programming?

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A solution is bounded if there exists a limit to the values that the decision variables can take, ensuring that the feasible region is closed and contains a finite number of corner points.

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What is the graphical method in Linear Programming?

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The graphical method is a technique used to solve linear programming problems with two variables by graphing the constraints, identifying the feasible region, and evaluating the objective function at the corner points.