OEM_DMOR_HW3 - OEM Class of 2009 DMOR Homework#3 Due...

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OEM Class of 2009 DMOR Homework #3: Due Saturday, October 6 th at the start of class. Question 1. Consider the following set of equations. x 1 + x 2 x 3 = 1 x 1 + 2 x 2 = 3 2 x 2 + x 3 + x 4 = 3 Part a: Calculate all extreme points of the feasible region given by those constraints, along with the restrictions that x ≥ 0. Do this by choosing every possible set of basic variables and solving three equations in three unknowns (not by graphing). Part b: Let x 1 , x 2 , and x 3 be basic, and solve for those variables in terms of the nonbasic variable x 4 . Now, suppose that you want to increase x 4 . How large can x 4 become before either x 1 , x 2 , or x 3 becomes negative? Part c: Take x 4 equal to the largest value allowed in part b, and adjust the values of x 1 , x 2 , and x 3 accordingly (using the fact that you’ve already solved for those basic variables in terms of x 4 ). Verify that this new solution corresponds to another one of the basic feasible solutions found in part a. Question 2.
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OEM_DMOR_HW3 - OEM Class of 2009 DMOR Homework#3 Due...

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