a7 - CO350 Assignment 7 Due: July 9 at 2pm. Your full name,...

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Unformatted text preview: CO350 Assignment 7 Due: July 9 at 2pm. Your full name, student ID number, the course number, and the name of your instructor should all be clearly visible on the front of your assignment. Exercise 1: For the following pairs ( A,b ) solve the feasibility problem ( Ax = b, x 0) by first formu- lating the auxiliary problem ( P ) and then solving ( P ) by the simplex method. Your solution should include the initial and final tableaux, but you do not need to include the intermediate tableaux required to solve ( P ). If ( Ax = b, x 0) is feasible, give a feasible solution, otherwise find a vector y satisfying ( A T y , b T y < 0). (a) A = - 1 1 2 1- 2 1 1- 1 1 1 1- 1 1 , and b = 1 1 4 . (b) A = 1 2 1- 1 1 1 1- 1 1 1 1 , and b = 1 3 1 . Exercise 2: Let A R m n with rank( A ) = m and b R m . Prove that, if ( x,u ) is an optimal basic feasible solution for the auxiliary problem ( P ) and ( x,u ) has objective value 0, then...
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