4. Write the standard primal and dual for each of the following problems: (a) Minimum z = 5x1 – 3x2 - Subject to X1 + x2 – 2x3 > 2 Зх, — х2 + хз 23 X1, X2, X3 2 0 (b) Minimum z = = 2x1 + x2 + 4x3 Subject to X1 + x2 + 2x3 2x1 + x2 + 3x3 = 5 X1, X2, X3 2 0 (c) Minimum z = 3x1 – 2x2 + 4x4 %3D Subject to 2x1 – x2 + 4x3 +x4 < 5 X1 + x2 + 2x3 < 4 2x1 – x2 + x3 > 1 X1, X2, X3, X4 2 0

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