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Dual as Minimum

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Please help with the following linear programming problems. Provide step by step calculations.

Consider the primal problem
Min c1x+ c2x2 + c3x3
s.t a11x1 + a12x2 + a13x3 >=b1
a21x1 + a22x2 + a23x3 >=b2
a31x1 + a32x2 + a33x3 >=b3
x1, x2 and x3 >=0

Form the dual problem.
Rewrite the dual as a minimum problem
Determine conditions on A, b, and c so that the dual is identical to the primal.
Give an example.

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Solution Summary

Dual as Minimum is clearly evaluated in this case. Step by step calculations are given in the solution.

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Dual Problem
Maximize W = b1 y1 + b2 y2 + b3 y3
Subject to a11 y1 + a21 y2 + a31 y3 <= c1
a12 y1 + a22 y2 + a32 y3 <= c2
a13 y1 + a23 y2 + a33 y3 <= c3
y1, y2 and y3 >=0
Dual as Minimum
Minimize W* =- b1 y1 - b2 y2 - b3 y3
Subject to a11 ...

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