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 the objective function in Linear Programming?

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The objective function is a mathematical expression that defines the goal of the linear programming problem, typically to maximize or minimize a quantity, such as profit or cost.

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What does the feasible region represent in Linear Programming?

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The feasible region is the set of all possible points that satisfy the constraints of a linear programming problem. It is typically represented graphically as a polygon.

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What is the significance of corner points in the feasible region?

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Corner points (or vertices) of the feasible region are significant because the optimal solution to a linear programming problem will occur at one of these points.

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What is a constraint in Linear Programming?

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A constraint is a condition that must be satisfied in a linear programming problem, usually expressed as a linear inequality or equation.

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What type of line is used to represent inequalities in Linear Programming graphs?

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Dashed lines are used to represent inequalities that do not include the boundary (e.g., < or >), while solid lines are used for inequalities that do include the boundary (e.g., ≤ or ≥).

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How do you determine the maximum value of an objective function?

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To determine the maximum value of an objective function, evaluate the function at each corner point of the feasible region and identify the highest value.

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What is the difference between a solid line and a dashed line in a graph of inequalities?

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A solid line indicates that the points on the line are included in the solution set (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

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What does it mean if a point is outside the feasible region?

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A point outside the feasible region does not satisfy all the constraints of the linear programming problem and is therefore not a viable solution.

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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.