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Homework10 - ENGRI 1101 Engineering Applications of OR Fall...

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ENGRI 1101 Engineering Applications of OR Fall ’08 Homework 10 Integer Programming Due date: 4:00pm on Monday, November 17, 2008 in the ENGRI 1101 box at the west end of the corridor on the second floor of Rhodes Hall, where it connects to Upson. Reading assignment: Handout 8 in the course packet and Chapter 9 of Winston (“Integer Program- ming”), also included in the course packet. Make sure to put your name and section on the cover page and staple the problems in order. 1. (35 points) Consider the following linear program: max 12 - 2 x 4 - x 2 + x 3 s . t . x 1 = 6 - x 4 - x 2 x 5 = 10 - x 4 - x 2 - 2 x 3 x 6 = 2 - x 4 - x 2 x 7 = 4 - x 2 x 1 , ..., x 7 0 (a) (20 points) Solve the linear program using the simplex method. (b) (15 points) Suppose we consider the integer program with the objective and constraints as above, with the additional requirement that x 1 ,...,x 7 be integers. Solve this integer programming problem. (Hint: think carefully before you work too hard!) Make sure you rigorously explain why your solution is an optimal one.
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