Problem 3 (30%): Consider the following problem. subject to and Maximize Z = 3x₁ + x₂ + 4x3, x₁ ≥ 0, X₂ ≥ 0, X3 ≥ 0. The

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Problem 3 30 Consider The Following Problem Subject To And Maximize Z 3x X 4x3 X 0 X 0 X3 0 The 1 (27.35 KiB) Viewed 25 times

Problem 3 30 Consider The Following Problem Subject To And Maximize Z 3x X 4x3 X 0 X 0 X3 0 The 2 (7.82 KiB) Viewed 25 times

Problem 3 (30%): Consider the following problem. subject to and Maximize Z = 3x₁ + x₂ + 4x3, x₁ ≥ 0, X₂ ≥ 0, X3 ≥ 0. The corresponding final set of equations yielding the optimal solution is: (0) 2 + 2x₂ + x + x = 17 subject to 6x₂ + 3x₂ + 5x3 ≤ 25 3x₂ + 4x₂ + 5x3 ≤ 20 (1) x₁ - x₂ + x₁ - x₁ = (2) x₂ + x3x₂ + x₁ = 3 a) Identify the optimal solution from this set of equations. b) Construct the dual problem. c) Identify the optimal solution for the dual problem from the final set of equations. Verify this solution by solving the dual problem graphically. d) Suppose that the original problem is changed to and Maximize Z = 3x₂ + 3x₂ + 4x3, 6x₂ + 2x₂ + 5x3 ≤ 25 3x₂ + 3x2 + 5x3 s 20
x₂ ≥ 0, X3 ≥ 0. x₁ ≥ 0, Use duality theory to determine whether the previous optimal solution is still optimal.