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 and constraints are linear.

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CCSS.8.EE.C.8B

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What is a 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. It represents all possible solutions.

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CCSS.HSA.REI.D.12

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What does the objective function represent in Linear Programming?

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The objective function is the function that needs to be maximized or minimized in a linear programming problem, typically representing profit or cost.

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CCSS.8.F.A.2

CCSS.HSF.IF.C.9

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What are constraints in Linear Programming?

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Constraints are the inequalities that define the limits within which the solution must lie in a linear programming problem.

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CCSS.8.EE.C.8B

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How do you write a system of inequalities?

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A system of inequalities consists of two or more inequalities that represent the constraints of a linear programming problem.

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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 occurs at one of these points.

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How do you determine the maximum profit in a Linear Programming problem?

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

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What is the graphical method in Linear Programming?

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The graphical method involves plotting the constraints on a graph to find the feasible region and then identifying the optimal solution visually.

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CCSS.8.EE.C.8B

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What is the difference between a strict inequality and a non-strict inequality?

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A strict inequality (e.g., < or >) does not include the boundary, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary.

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CCSS.6.EE.B.8

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What does it mean to maximize an objective function?

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To maximize an objective function means to find the highest possible value of that function within the constraints of the problem.