Formulating a Linear Programming Problem (Edexcel A-Level Further Mathematics): Quizzes

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Formulating a Linear Programming Problem
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What is the primary purpose of Linear Programming?

To optimize an objective function

Which type of variable is added to a \leq constraint to convert it into an equation?

Slack variable

Which type of variable is subtracted from a \geq constraint to convert it into an equation?

Surplus variable

For which types of constraints are artificial variables introduced?

\geq or == constraints

What does a slack variable represent in a constraint?

Unused capacity

What does a surplus variable represent in a constraint?

Excess quantity

How is the constraint 2x+3y102x + 3y \leq 10 converted to an equation using a slack variable?

2x+3y+s=102x + 3y + s = 10

How is the constraint x+4y12x + 4y \geq 12 converted using a surplus variable ss?

x+4ys=12x + 4y - s = 12

What constraint must always be included for all decision and added variables?

They must be non-negative

In an objective function Z=ax+byZ = ax + by, what do the coefficients aa and bb represent?

Each variable's contribution

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