Verify the Duality Theorem 4.1.9 on each of the followingLOPs.a.Max. z= −211x1 −189x2 −106x3 −175x4s.t. 4x1 +6x2 −5x3 +3x4 ≤ 22x1 +4x3 +9x4 ≤ 18−3x1 +2x2 −2x3 ≤ 275x2 −2x4 ≤ 232x1 −x2 −x3 +x4 ≤ 167x1 +8x2 −7x3 +4x4 ≤ 12& x1, x2, x3, x4 ≥ 0b.Max. z = x1 + 2x2s.t. 17x1 + 21x2 ≤ 51x1 − 4x2 ≤ 123x1 + 6x2 ≤ 14& x1 , x2 ≥ 0
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