Graphical Solution of LP problems (Edexcel A-Level Further Mathematics): Quizzes

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Solving a Linear Programming Problem Graphically
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What are the two key methods for solving linear programming problems graphically?

Objective Line & Vertex Methods

What term describes the conditions x,y0x, y \geq 0 in linear programming?

Non-negativity conditions

What is the feasible region in linear programming?

Where all constraints overlap

How do you plot constraints for graphical solutions?

Convert inequalities to equalities

In the Vertex Method, where is the objective function evaluated?

At each vertex of feasible region

In Example 1, what is ZZ at vertex (2,4)(2, 4) for Z=3x+5yZ = 3x + 5y?

Z=26Z = 26

What is the maximum value of Z=3x+5yZ = 3x + 5y in Example 1?

Z=30Z = 30 at (0,6)(0, 6)

What point gives the optimal integer solution in Example 2?

(2,4)(2, 4) with Z=36Z = 36

Which common mistake involves forgetting x,y0x, y \geq 0?

Omitting non-negativity

What should you test when integer solutions are required?

Lattice points in feasible region

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