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An optimization problem:

$$\text{ maximize } z=8x+6y$$ $$\text{ such that: } x-y ≤ 0.6 \text{ and } x-y≥2$$

Show that it as no feasible solution using SIMPLEX METHOD.

It seems very logical that it has no feasible solution(how can a value be less than $0.6$ and greater than $2$ at the same time). When I tried solving it using simplex method, I found that it has an unbounded solution(as corresponding to the maximum(positive) value of $c_j − z_j $, all values in the corresponding column were either negative or zero).

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    $\begingroup$ The region is empty, as you point out. There are no values of $z$ to consider. $\endgroup$ – lulu Oct 28 '17 at 12:26
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    $\begingroup$ maximize $z$ over the empty set :P $\endgroup$ – Zubin Mukerjee Oct 28 '17 at 12:26
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    $\begingroup$ @lulu can you please prove it through simplex method ? $\endgroup$ – SmoKer Oct 28 '17 at 12:29
  • $\begingroup$ use the Two-Phases Simplex Algorithm $\endgroup$ – Marcello Sammarra Oct 28 '17 at 19:49
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    $\begingroup$ Can you learn from this solved problem and show us where you got stuck? If you can solve this problem after reading this, you may answer your own question and accept it, so that we can upvote it. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Mar 5 '18 at 23:31
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you will get $$2\le x-y\le \frac{3}{5}$$ which is impossible.

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