Determine the dual of each of the following linear programmi

Determine the dual of each of the following linear programming problems:

1. Minimize 6x₁ + 12x₂ - 18x₃

subject to    x₁ - 3x₂ + 6x₃ = 30   2x₁ +8x₂ - 16x₃ =70   x₁, x₂ 0, x₃ unrestricted

2. Maximize x₁ - 7x₂ +3x₃

subject to 2x₂ +5x₃ = 20 8x₁ - 3x₃ = 40 x₂ +4x₃ 60 x₁,x₃ 0, x₂ unrestricted

Solution