Simplex Algorithm (Edexcel A-Level Further Mathematics): Flashcards

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Two-stage Simplex Method
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When is two-stage Simplex method used?

For LP problems with \geq or equality constraints

What are artificial variables?

Temporary variables (t1,t2,...t_1, t_2, ...) for initial feasible solution

When must artificial variables be eliminated?

By end of Stage 1

Objective of Stage 1 in two-stage Simplex

Minimise sum of all artificial variables

Objective of Stage 2 in two-stage Simplex

Solve original problem from Stage 1's feasible solution

Variable subtracted in \geq constraints

Surplus variable (ss)

Convert a1x1+a2x2ba_1x_1 + a_2x_2 \geq b to equation

a1x1+a2x2s+t=ba_1x_1 + a_2x_2 - s + t = b

Auxiliary objective function WW equals

Sum of all artificial variables

What does W=0W=0 after Stage 1 indicate?

A feasible solution

Error: using auxiliary objective in Stage 2

Should use original objective function, not WW

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