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 profit or minimize 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 are corner points (vertices) in the context of Linear Programming?

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Corner points (or vertices) are the points at which the edges of the feasible region intersect. These points are critical for finding the optimal solution.

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How do you determine the maximum or minimum value of the objective function?

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To determine the maximum or minimum value of the objective function, evaluate the objective function at each corner point of the feasible region and compare the results.

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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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What does the inequality x + y ≤ 8 represent?

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The inequality x + y ≤ 8 represents a constraint where the total number of purses (small and big) that Sarah can make in a week cannot exceed 8.

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What is the significance of the slope in a linear inequality?

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The slope in a linear inequality indicates the rate of change of one variable with respect to another. It helps in graphing the inequality and understanding the relationship between the variables.

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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.

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What does the inequality y ≥ -3/4 x + 3 indicate about the graph?

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The inequality y ≥ -3/4 x + 3 indicates that the region above the line y = -3/4 x + 3 is included in the solution set.