1. Give the dual of each of the following linear programs: (a) maximize 100x1 + 200x2 + 300x3 + 400x4 (b) subject to x12x2 3x3 - 4x4 10, -5x16x27x3+8x4-20, 9x110x211x3 - 12x4 = 30, x1,x30, x40, x2 unrestricted maximize 4 subject to x4x12x2+4x3, x4 -2x13x2-5x3, x43x14x2+6x3, x1 + x2 x3 = 1, x1, x2, x30, x4 unrestricted