Find the dual optimization problem to the following linear programming
min 3x_{1}-2x_{2} subject to x_{1}+x_{2}<1 3x_{1}-4x_{2}\le-2 x_{2}<-1
(i) max subject to -\lambda_{1}+2\lambda_{2}+\lambda_{3} \lambda_{1}+3\lambda_{2}=-2 \lambda_{1}-4\lambda_{2}+\lambda_{3}=3 \lambda_{1}\ge0,\lambda_{2}\ge0,\lambda_{3}\ge0
(iii) max \lambda_{1}+2\lambda_{2}-\lambda_{3} subject to \lambda_{1}+3\lambda_{2}=-3 \lambda_{1}-4\lambda_{2}+\lambda_{3}=2 \lambda_{1}\ge0,\lambda_{2}\ge0,\lambda_{3}\ge0
(ii) max subject to -\lambda_{1}+2\lambda_{2}+\lambda_{3} \lambda_{1}+3\lambda_{2}=-3 \lambda_{1}-4\lambda_{2}+\lambda_{3}=2 {}_{1}\ge0,\lambda_{2}\ge0,\lambda_{3}\ge0
(iv) max \lambda_{1}+2\lambda_{2}-\lambda_{3} subject to \lambda_{1}+3\lambda_{2}=2 \lambda_{1}-4\lambda_{2}+\lambda_{3}=-3 \lambda_{1}\ge0,\lambda_{2}\ge0,\lambda_{3}\ge0
