Exercise 2.9 For the following pair of primal-dual problems, determine whether the listed solutions are optimal. min 2a1 + 3x2 2x1 + 3x2 < 30 Tị + 2x2 > 10 max -30y1 + 10y2 -2y1 + -3y1 + + y3 < 2 - y3 < 3 2y2 x2 2 0 Y1, Y3 2 0. x2 2 0 (a) #1 10, x2 = ; Y1 = 0, y2 = 1, y3 = 1. (b) a1 = 20, x2 = 10; y1 = -1, y2 = 4, y3 = 0. 10. %3D (c) ¤1 10 #2 = ; y1 = 0, y2 = }, ys = }. %3D %3D

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