Section 3.1 - Standard Form and Pivoting

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5 Terms

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  • Minimize the objective function

  • Equality Constraints

  • Nonnegative variables

What are the requirements for Standard Form (SF)?

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Min z(x) = d + c^{T}x

s.t. Ax = b

x \geq 0

Write out what a SF problem would look like in matrix-vector form?

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True

T/F: Can ALL linear programs be converted to SF?

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Using nonnegative slack/surplus variables

How can you convert inequalities to equalities?

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<p>Simplex Tableau</p><p></p><p>-d = optimal solution</p><p>b = constraints</p><p>A = linear program</p><p>$$c^{T}$$ = objective function row</p><p></p><p>minimize is assumed</p><p>nonnegative $$\bar{x}$$ is assumed</p>

Simplex Tableau

-d = optimal solution

b = constraints

A = linear program

c^{T} = objective function row

minimize is assumed

nonnegative \bar{x} is assumed

What is the shorthand format for an LP in SF?

What does it look like?

Label all parts of the format.

Bonus points: What are two assumptions we can make about format?