Is it possible for a certain variable to have zero coefficient at objective function ?

For example, can I have

Z= x while my decision variable is x and y?

  • 2
    $\begingroup$ Yes, You can even make all objective coefficients zero, In that case the LP solver will stop as soon as a feasible solution is found. $\endgroup$ – Erwin Kalvelagen May 31 '18 at 16:18

Yes, in fact this is a frequent situation. You can thus define utility variables to use for your constraints only.

  • $\begingroup$ If the coefficient of y is zero at objective function, this means no matter what the value of y is, the optimal value is unaffected right ? $\endgroup$ – Ling Min Hao May 31 '18 at 16:05
  • 1
    $\begingroup$ This is not necessarily true. Consider the problem $\min y$ subject to $y\geqslant x$ and $x,y\geqslant0$. The coefficient of the variable $x$ in the objective function is zero, but if we set $x=5$, the optimal objective value is $5$, while if we set $x=10$, the optimal objective value is $10$. $\endgroup$ – David M. May 31 '18 at 23:43

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