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, often used for maximizing profit or minimizing costs.

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What is the feasible region in Linear Programming?

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The feasible region is the area on a graph where all the constraints of a linear programming problem overlap, representing all possible solutions.

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What is an objective function?

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An objective function is a mathematical expression that defines the goal of a linear programming problem, typically to maximize or minimize a quantity.

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How do you identify the vertices of the feasible region?

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Vertices of the feasible region can be found by solving the system of inequalities that define the constraints of the linear programming problem.

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What does it mean to maximize profit in Linear Programming?

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Maximizing profit means finding the combination of variables that results in the highest possible profit, as defined by the objective function.

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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, often represented as an inequality.

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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 is the significance of the vertices in the feasible region?

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The vertices of the feasible region are significant because the optimal solution to a linear programming problem will always occur at one of these vertices.

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What is the profit for each balsam fir tree in the FFA Club example?

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The profit for each balsam fir tree is $15.

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What is the profit for each Douglas fir tree in the FFA Club example?

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The profit for each Douglas fir tree is $18.