Practice Prelim 1

Practice Prelim 1 - PRELIM 1 ORIE 3310/5310 February 19,...

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PRELIM 1 ORIE 3310/5310 February 19, 2009 Closed book exam. Justify all work. 1. Consider again the the following problem from the homework assignment. The standard decomposition procedure is applied using two subproblems (SUB1, SUB2): ORIGINAL PROBLEM max 6 x 1 + 4 x 2 + 3 x 3 + 3 x 4 s.t. x 1 + x 2 + x 5 3 - x 2 + x 3 + x 4 - x 5 5 2 x 1 + x 2 4 x 1 + x 2 + x 3 6 x 4 + x 5 3 x 4 + 2 x 5 4 x 1 , x 2 , x 3 , x 4 , x 5 0 We begin the solution procedure with a restricted master program consisting of slack variables s 1 and s 2 associated with the two linking constraints and variables λ 1 and μ 1 corresponding, respectively, to the two subproblem solutions ( x 1 , x 2 , x 3 ) = (0 , 0 , 0) and ( x 4 , x 5 ) = (0 , 0) . At a later stage of the computation the following tableau for the restricted master program is encountered. basis λ 1 λ 2 μ 1 μ 2 s 1 s 2 r.h.s. ( - z ) - 12 0 0 0 0 - 3 - 27 s 1 - 2 0 0 0 1 0 1 μ 2 - 4 / 3 0 0 1 0 1 / 3 1 / 3 λ 2 1 1 0 0 0 0 1 μ 1 4 / 3 0 1 0 0 - 1 / 3 2 / 3 (a) (5 points) Write the initial restricted master as speciFed above. (b) (5 points) Determine by inspection the inverse of the basis matrix (i.e.,
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This note was uploaded on 10/29/2011 for the course ORIE 3310 taught by Professor Bland during the Spring '08 term at Cornell.

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Practice Prelim 1 - PRELIM 1 ORIE 3310/5310 February 19,...

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