Consider the following optimization model min 6x1 + 8x2 + 5x3 s.t. x1 + 2x2 + x3 ≥ 3 x1 + x2 ≥ 2 x1, x2 ≤ 0 x3 ≥ 0 a) State the dual of the model b) Solve the dual model raised in a) c) Using the solution of b), determine, if possible, the solution of the primal model. Justify.

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Consider the following optimization model

min 6x1 + 8x2 + 5x3

s.t. x1 + 2x2 + x3 ≥ 3

x1 + x2 ≥ 2

x1, x2 ≤ 0

x3 ≥ 0

a) State the dual of the model
b) Solve the dual model raised in a)
c) Using the solution of b), determine, if possible, the solution of the primal model.
Justify.

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