IOE310_PS06_Solution (1) - IOE 310 Problem Set 06 Solution...

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IOE 310 - Problem Set 06 Solution Suggested Reading Section 4.14 (p.184-186) (skip Example 9) Section 6.1 Section 6.2 (ignore (10”)’ for artificial variables on p.272) Problem 1 Section 4.14 Problem 4 (p.189) Professor Kaufman Comments: I disagree with the solution for Problem 1, which I post below. I am interested in seeing your solutions. If you have a solution, please give it. If you agree with the solution’s manual, please give the same solution but with added justification. The part I don’t understand is: why can a BFS not have both z’ and z” be positive? Justify this. Otherwise, if you disagree with the solutions manual, please justify why you disagree - a counter-example perhaps. You will receive full credit too if you just copy the answer below. However, I would rather you think. The solution from the textbook is: max z = z + z s.t 4 x 1 + x 2 4 2 x 1 x 2 0 . 5 2 x 1 3 x 2 = z z All variables non-negative First note that in any basic feasible solution, z and z cannot both be positive. Then observe that if 2 x 1
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