Question: Consider the following problem Maximize Z= -x 1 2x 2 x 3 Subject to x 1 + x 2 + 2x 3 12 x 1

Consider the following problem

Maximize Z= -x₁ 2x₂ x₃

Subject to

x₁ + x₂ + 2x₃ 12

x₁ + x₂ x₃ 1

and

x₁0, x_²0 , x₃0

a. Construct the dual problem

b. Use duality theory to show that the optimal solution for the primal problem has Z 0 (Please show the step by step solution here in simplex method using row operations. Ex: R₁+R₂₌R_2(new) )

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