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Formulate as a linear optimization problem. For given numbers a and b find two numbers x and y whose difference is at most 1, such that |x −a|+|y −b| is minimal.

So far I know that |x −y| $\le$ 1 but I am not sure where to go next.

stackdsewew
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1 Answers1

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$$ \mbox{Minimize }\; Z=\omega_1+\omega_2 $$ subject to $$ x-y\le 1\\ -x+y \le 1 \\ x-a\le \omega_1 \\ -x+a \le \omega_1\\ y-b\le \omega_2 \\ -y+b \le \omega_2\\ $$

Kuifje
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