Problem 2 (10 pt.) Find the dual problem of the following linear programs: (1) max x₁ + 2x₂ + 3x3 + 4x4 s.t. -x₁ + x₂-x3-3x4 = 5, 6x₁ +7x2 + 3x3-5x4 ≥ 8, (2) min s.t. 12x1-9x29x3 + 9x4 ≤ 20, X1, X₂ ≥ 0, X3 ≤0, x4 unrestricted. 3x₁ + 2x₂ + x3 3x₁ + x₂ + x3 ≥ 3, - 3x₁ + 3x₂ ≥ 6, x2 + x3 ≤ 3, x₁ ≥ 0, x₂ ≤ 0, x3 unrestricted.

Fig: 1