# hw6 - CO 227 Homework assignment 6 Fall `10 Page 1 CO 227...

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CO 227 - Homework assignment 6 Fall ‘10 Page 1 CO 227 - Fall ‘10 Homework assignment #6: (Due at 5pm, on Monday, Dec 6th) 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 = 90 points Question 1 - Branch-and-bound (30 points) Consider the following integer program: max z = x 1 +5 x 2 s.t. - 4 x 1 +3 x 2 6 3 x 1 +2 x 2 18 x 1 , x 2 0 and integer (IP) The picture below shows the branch-and-bound tree in the middle of solving this problem (only the nodes that were already explored are shown). Subp. 1 z * = 28 . 94 x * 1 = 2 . 47 x * 2 = 5 . 29 Subp. 2 z * = 25 . 5 x * 1 = 3 x * 2 = 4 . 5 Subp. 4 INFEASIBLE Subp. 5 z * = 23 . 33 x * 1 = 3 . 33 x * 2 = 4 Subp. 6 z * = 19 x * 1 = 4 x * 2 = 3 Subp. 7 z * = 23 x * 1 = 3 x * 2 = 4 Subp. 3 z * = 25 . 33 x * 1 = 2 x * 2 = 4 . 67 x 1 3 x 1 2 x 2 5 x 2 4 x 1 4 x 1 3 (a) (3 points) Suppose that we know z 2

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