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hw5 - CO 227 Homework assignment 5 Fall ‘10 Page 1 CO 227...

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Unformatted text preview: CO 227 - Homework assignment 5 Fall ‘10 Page 1 CO 227 - Fall ‘10 Homework assignment #5: (Due at the beginning of the class, 10:30AM, on Friday, Nov 19th) Instructions: • Please show all your work and justify your answers. Answers without proper justification will not be considered. • Please list who you collaborated with. • Please staple your homework and write your name and student id in pen. • Total value = 108 points Question 1- Duality (16 points) Consider the following LP: max (4 , 1 , 6 , 7 , 2) x s.t. 2 8- 1 3- 1 4 5 3 5 1 x ≥ ≤ ≤ 5- 1 6 x ≥ (1) (a) (5 points) Find the dual of (1) (b) (11 points) Notice that ¯ x = (0 , 5 , 1 , , 0) is feasible for (1). Argue, using the knowledge about duality and the dual you found in part (a) that problem (1) is unbounded. (I do NOT want you to use the simplex method to do this question!) Question 2- Duality and complementary slackness (13 points) Consider the following LP: min x 1- 2 x 2 + x...
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hw5 - CO 227 Homework assignment 5 Fall ‘10 Page 1 CO 227...

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