s02rec09

# s02rec09 - Recitation 9 Problems More Practice Problems for...

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Recitation 9 Problems More Practice Problems for Midterm II These problems are intended to aid in your understanding of the topics. Please make sure you also understand everything from the practice midterm. 15.053 Introduction to Optimization April 19,2002 1. Consider the following linear program. M a xz=-4 x 1 +x 2 +2 x 3 s.t. x 2 x 3 <= 4 -x 1 +3 x 3 <= -1 -2x 1 -3 x 2 <= -2 x 1 ,x 2 3 >= 0 a) Formulate the dual of the above linear program b) Use duality to show that the optimal objective function value of the primal problem is 0. (Hint: Find a feasible point.) 2. Consider the following network flow problem, where the arcs are defined with (u ij , c ij ), and the lower bounds are 0: Find the optimal flows using the network simplex method. Use the following spanning tree (the dashed line indicates nonbasic flow at its upper bound. All other nonbasic flows are at the lower bound):

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3. The US Olympic Team is trying to put together a relay team for the 400-meter relay. Each swimmer must swim 100 meters of breaststroke, backstroke, butterfly or freestyle.
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## This note was uploaded on 12/20/2011 for the course BUS 15.053 taught by Professor Prof.jamesorlin during the Spring '05 term at MIT.

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s02rec09 - Recitation 9 Problems More Practice Problems for...

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