Linear Program. Practice

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What is a linear program?

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A linear program is a mathematical method for determining a way to achieve the best outcome in a given mathematical model, often involving maximizing or minimizing a linear objective function subject to linear equality and inequality constraints.

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What does the objective function represent in linear programming?

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The objective function represents the goal of the linear programming problem, which is to maximize or minimize a certain quantity, such as profit or cost.

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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, typically expressed as a linear inequality or equation.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a boundary line, then shade the region that satisfies the inequality (above or below the line depending on the inequality sign).

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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 all constraints in a linear programming problem, representing all potential solutions.

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What is the corner point method in linear programming?

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The corner point method involves evaluating the objective function at each vertex (corner point) of the feasible region to find the maximum or minimum value.

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What is the significance of the maximum and minimum values in linear programming?

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The maximum and minimum values represent the best possible outcomes (e.g., maximum profit or minimum cost) that can be achieved within the constraints of the problem.

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What is the role of non-negativity constraints in linear programming?

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Non-negativity constraints ensure that the decision variables in a linear programming problem cannot take negative values, which is essential in real-world scenarios like production.

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How do you set up a linear programming problem?

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To set up a linear programming problem, define the decision variables, formulate the objective function, and establish the constraints based on the problem context.

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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 and identifying the feasible region.