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

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Formulating a Linear Programming Problem
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What is Linear Programming (LP)?

A mathematical method to optimize an objective function subject to constraints

What is the purpose of the objective function in LP?

Maximise profit or minimise cost

When are slack variables added?

To \leq constraints to convert them into equations

What do slack variables represent?

Unused capacity

When are surplus variables used?

Subtracted from \geq constraints to make equations

What do surplus variables represent?

Excess quantity

When are artificial variables introduced?

For \geq or == constraints to start Simplex algorithm

What is the nature of artificial variables?

Temporary, eliminated during optimisation

Convert ax+bydax + by \leq d using slack ss

ax+by+s=dax + by + s = d where s0s \geq 0

Convert ax+bydax + by \geq d using surplus ss

ax+bys=dax + by - s = d where s0s \geq 0

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