Question: Consider the following integer program: Maximize Z = 2x1 + 4x2 + 5x3 + 3x4 s.t. 3x2+2x3 + 2x4 7 6x1+ 5x2 + 5x3

Consider the following integer program: Maximize Z = 2x1 + 4x2 + 5x3 + 3x4 s.t. 3x2+2x3 + 2x4 7 6x1+ 5x2 + 5x3 + 2x416 8x2 + 6x3 + 7x4 10 X1, X2, X3, X4 20 integer Parts (a) - (c) below are independent of each other. You are given three fractional solutions which are feasible for the LP-relaxation of the problem. For each of the fractional points, give a cutting plane that will cut off the fractional solution. a) (0, 2.5, 0, 0) b) (0.3, 0.3, 2.5, 0) c) (0, 0, 0.5, 1) (1) (2) (3)

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