Let us consider a linear programming problem shown below: min x f ( x ) − c where, f ( x ) is a linear function of x. Now, can be following maximization problem be considered as an equivalent to the above minimization problem? max x ( 1 f ( x ) − c )

Question

Let us consider a linear programming problem shown below:                              min          x                f        (        x        )        −        c            where,   f  (  x  ) is a linear function of   x. Now, can be following maximization problem be considered as an equivalent to the above minimization problem?                              max          x                          (                      1                          f              (              x              )              −              c                                )

ele5ph1a7jl1 · Accepted Answer

It seems to work only if  f  (  x  )  −  c  &amp;gt;  0    ∨    f  (  x  )  −  c  &amp;lt;  0Indeed if   f  (  x  ) is increasing, that is       f    ′    (  x  )  &amp;gt;  0, we have that       1          f      (      x      )      −      c       is decreasing, since            (              1                  f          (          x          )          −          c                    )        ′    =            −              f        ′            (      x      )              (      f      (      x      )      −      c              )        2              &amp;lt;  0and if   f  (  x  ) is decreasing that is       f    ′    (  x  )  &amp;gt;  0 we have that       1          f      (      x      )      −      c       is increasing.

Let us consider a linear programming problem shown below: <mtable columnalign="right left rig

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