Linear Programming

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What is Linear Programming?

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A method for finding a maximum or minimum value of some quantity, given a set of constraints.

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What are the vertices of the feasible region in a linear programming problem?

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The points where the constraints intersect, which define the boundaries of the feasible region.

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What is the objective function in linear programming?

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A mathematical expression that defines the quantity to be maximized or minimized, typically represented as P = ax + by.

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What is the feasible region in linear programming?

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The area on a graph where all constraints overlap, representing all possible solutions.

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What does it mean to maximize a function in linear programming?

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To find the highest possible value of the objective function within the feasible region.

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What does it mean to minimize a function in linear programming?

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To find the lowest possible value of the objective function within the feasible region.

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How do you graph constraints in linear programming?

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By plotting the inequalities on a graph and shading the appropriate regions.

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What is an inequality in the context of linear programming?

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A mathematical statement that shows the relationship between two expressions, often used to define constraints.

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What is the significance of the intercepts in linear programming?

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Intercepts help to identify the feasible region and the vertices of the constraints.

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What is a constraint in linear programming?

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A condition that must be satisfied for a solution to be valid, often expressed as an inequality.