EN.625.415 Midterm: Exam 2 Solutions Fall 2012
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Problem 1: consider the following linear program: (lp) min 4x1 x2 3x3 + 3x4 s. t. X1 + 3x2 + 5x3 2x4 = 7 x1, x2, x3, x4 0. The optimal objective function value of (lp) is 51. 16 , and the optimal basis consists of the third and fourth columns; the matrix b and its inverse are. 32 : (5 points) compute the optimal solution for the dual problem of (lp). Solution: y t =h 3 3 i " 2. 32 i : (5 points) compute the the optimal objective function value of (lp) if we change the right computation must clearly utilize your answer from part a) in the manner illustrated in lecture. 1(cid:3). (note: the optimal basis does not change. ) For any credit, your hand side (cid:2) 5. Solution: the new optimal objective function value of (lp) will be 51. Problem 2: (10 points) consider (lp) min ct x s. t.
