solutionmidtermdecember11th2010

# solutionmidtermdecember11th2010 - This exam consists of 3...

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4. ( 5 points) Explain why you could have seen the solution immediately without doing all the calculatioins. Solution 1. First write optimization problem in standard form max - x 1 - x 2 +2 x 3 - 5 x 1 - 3 x 2 - x 3 - 10 - x 1 - x 2 - 2 x 3 - 1 x 2 3 x 1 x 2 x 3 0 Starting dictionaire has the form x 4 = - 10 +5 x 1 +3 x 2 + x 3 x 5 = - 1 + x 1 + x 2 +2 x 3 x 6 = 3 - x 2 z = 0 - x 1 - x 2 +2 x 3 This dictionaire is not primal feasible since the basic solution (=set nonbasic variables equal to 0 ) is not primal feasible. This means geometrically that the vertex 0 belonging to the above dictionaire does not belong to the feasible region. 2. We need to apply the two-phase simplex method. To determine a primal feasible start dic- tionaire representing a primal feasible vertex we need to solve the Help problem max - x 0 - x 0 - 5 x 1 - 3 x 2 - x 3 - 10 - x 0 - x 1 - x 2 - 2 x 3 - 1 - x 0 + x 2 3 x 0 x 1 x 2 x 3 0 2
Introducing the slack variables x 4 , x 5 and x 6 we obtain the (not primal feasible) start dictio- naire x 4 = - 10 + x 0 +5 x 1 +3 x 2 + x 3 x 5 = - 1 + x 0 + x 1 + x 2 +2 x 3 x 6 = 3 + x 0 -

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