February 11, 2006` QUIZ 2 1. Write the dual of the following LP problem Maximize z = 5x1 + 6x2 Subject to x1 + 2x2 = 5 -x1 + 5x2 3 x1 is unrestricted and x2 0 2. The primal solution of an LP maximization problem is as follows. Cb BV 2 x2 5 x3 0 s3 Z zj 1350 cj-zj cj 3 Xb x1 100 -0.25 230 1.50 20 2 7 -4 2 x2 1 0 0 2 0 5 x3 0 1 0 5 0 0 0 0 s1 s2 s3 0.5 -0.25 0 0 0.5 0 -2 1 1 1 2 0 -1 -2 0 The primal problem is as follows Maximise z = 3x1 + 2 x2 + 5x3 Subject to x1 + 2x2 + x3 < 430 3x1 + 2x3 < 460 x1 + 4x2 < 420 and all x1, x2 & x3 > 0 The management has increased all resources by 30 %. Find out whether the solution still holds good. Give p roper explanation.