Math 364 Midterm

Math 364 Midterm - Math364(Fall 2013 Midterm 1 Principles...

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Math364 (Fall 2013) – Midterm 1 Principles of Optimization (Fall 2013) Midterm Examination Name: WSU ID: There are six problems in this exam. The total points (given in parentheses) add to 105. You will be graded for 100. Space given here should be sufficient to do all necessary work, but in case you use any extra sheets of paper for rough work, write your name on each such sheet, and attach all such sheets to this exam before submitting. Time is precious – try to first finish problems that you are sure of. Good luck! 1. (15) Suppose we have the following tableau in canonical form for a maximization LP. z x 1 x 2 x 3 x 4 x 5 x 6 rhs 1 0 0 0 c 1 c 2 c 3 z * 0 0 - 2 a 3 a 5 - 1 0 0 0 1 a 1 0 - 3 0 a 7 2 0 0 a 2 a 4 - 4 a 6 a 8 b State conditions on a 1 , . . . , a 8 , b, c 1 , c 2 , c 3 and z * that make the following statements true: (a) The current bfs is optimal, and there are alternative optimal solutions, but no alternative optimal bfs s . (b) The current tableau is feasible, but not optimal, and x 4 can enter the basis. In this case, what will be the value of

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