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Q39Section II (Mathematics)39 of 190

Constructing the dual of a three-constraint LPP

Consider the LP problem Max Z=x1−x2+3x3Z=x_1-x_2+3x_3 subject to x1+x2+x3≤10,2x1−x2−x3≤2,2x1−2x2−3x3≤6, x1,x2,x3≥0x_1+x_2+x_3\le10, 2x_1-x_2-x_3\le2, 2x_1-2x_2-3x_3\le6,\ x_1,x_2,x_3\ge0. Then the dual, Min W:py1+qy2+ry3W:py_1+qy_2+ry_3 subject to ay1+by2+cy3≥1,y1−y2−2y3≥−1,y1−y2−3y3≥3ay_1+by_2+cy_3\ge1, y_1-y_2-2y_3\ge-1, y_1-y_2-3y_3\ge3 and y1,y2,y3≥0y_1,y_2,y_3\ge0, has:

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