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Quiz.02.exam

# Quiz.02.exam - finding the optimal solution True or False...

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March 01, 2005 IE 5623 Quiz II Name: Please provide brief answers to the following questions. Question 5 is worth 60 points questions 1-4 are worth 10 points each. 1) Any linear programming problem can be transformed into an equivalent model as a convex combination of all of the extreme points of its constraint set. True or False? Explain briefly. 2) Consider the LP ( b Ax cx s.t. Min ). If the convex set formed by b Ax has one or more extreme directions, then the LP has an unbounded optimal solution. True or False? Explain briefly. 3) Consider the LP ( b Ax cx s.t. Min ) and the set of extreme points of b Ax . If the simplex algorithm starts with the basis that corresponds to the largest cx value, then it is possible that, in worst case, the simplex algorithm will visit all the extreme points before

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Unformatted text preview: finding the optimal solution. True or False? Explain briefly. 4) A degenerate optimal basis for an LP model always indicates alternative optimal solutions. True or False? Explain briefly. The following is the current simplex tableau of a linear programming problem. The objective is to minimize 6 5 4 2 2 x x x and x 1 , x 2 and x 3 are the slack variables. z 1 x 2 x 3 x 4 x 5 x 6 x RHS z 1 b c 0 0 h g-14 6 x 0 2 0 3 / 14 0 1 1 a 2 x 0 3 d 2 0 2 / 5 0 5 4 x 0 0 e f 1 2 0 0 5- a)Find the values of unknowns a through h in the tableau. ( Hint : Start from a and continue in alphabetic order) b) Identify B-1 matrix from the tableau (do not make any computations). c) Find 3 6 5 1 2 , , b x x z x x from the tableau....
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