1. Give the dual of each of the following linear programs: (a) 100x1200x2 + 300x3 + 400x4 maximize subject to x12x2 3x3 - 4x4 ≤ 10, -5x16x27x3+8x4 -20, 9x110x211x3 - 12x4 = 30, (b) maximize X4 subject to X1, X30, x4≤0, x2 unrestricted x4x12x2+4x3, x42x13x2 - 5x3, x43x14x2+6x3, x1 + x2 x3 = 1, x1, x2, x30, x4 unrestricted Hint: Remember to first rewrite all the constraints so that all variables are on the left and the right-hand side is a constant.

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