prelim2_ProblemSet

# prelim2_ProblemSet - ORIE 320/520 Tuesday November 7 2006...

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ORIE 320/520 PRELIM 2 Fall 2006 Tuesday November 7, 2006 7:30–9:00pm 90 minutes 1. (a) [2 marks] Deﬁne what we mean when we say a sequence of tableaux generated by the simplex method is cycling . (b) [2 marks] While the simplex method is cycling, can any of the basic feasible solutions produced be nondegenerate? Justify your answer, based on your deﬁnition in part (a). (c) [4 marks] Solve the following linear program by the simplex method ( NOT the revised simplex method), using the smallest subscript rule for entering and leaving variables. Begin with the basis [3 , 4 , 5]. State which basic feasible solutions you encounter are degenerate, and which pivots you perform are degenerate. maximize x 1 + 2 x 2 subject to x 1 - x 2 + x 4 = 0 2 x 1 - x 2 + x 3 = 0 x 2 + x 5 = 2 x 1 , x 2 , x 3 , x 4 , x 5 0 . 1

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2. Consider the following linear program. maximize - 2 x 1 + x 2 subject to x 1 + x 2 + 2 x 3 = 7 2 x 1 + x 2 + 3 x 3 = 10 x 1 , x 2 , x 3 0 . Consider the list of indices
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prelim2_ProblemSet - ORIE 320/520 Tuesday November 7 2006...

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