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Unformatted text preview: CO 227  Homework assignment 3 Fall 10 Page 1 CO 227  Fall 10 Homework assignment #3: (Due at Monday, Oct 18th, at 4pm) 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 = 100 points Question 1 Simplex method (100 points) Consider the following feasible LPs. For each of them, either obtain an optimal solution by providing a certificate of optimality or show that the LP is unbounded by providing a certificate of unboundedness. Show all your work by rewriting the LP in canonical form at each step. You may have several choices for variables entering/leaving the basis. However, to make the correction easier, if there is a choice, always choose the lowest index variable. If you do not do that, you will be penalized. (a) (50 points) max z ( x ) = (1 , 4 , 1 , 3 , , 0) x s.t. parenleftbigg 1 2 3 2 1 2 1 2 1 parenrightbigg x 1 x 2 x 3 x 4 x 5 x 6 = parenleftbigg 1 1 parenrightbigg x vector (1) Start with the basis B = { 5 , 6 } . Solution: Choose a nonbasic variable with c k > 0. Since there are several choices, we choose x 1 to enter the basis. Keeping x 2 , x 3 , x 4 = 0, we have parenleftbigg 1 2 parenrightbigg t + parenleftbigg x 5 x 6 parenrightbigg = parenleftbigg 1 1 parenrightbigg So t = min i : A ik...
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This note was uploaded on 01/18/2011 for the course CO 227 taught by Professor 1 during the Spring '10 term at Waterloo.
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