I have a following problem:

If I have some function $aX+bY+cZ+mD+nF$ and I want to maximize it and have some constraints, how can I find ALL solutions for this maximum value of the function?

To sum up: I have a function value (e.g. $100$) and I have one optimal solution ($a,b,c,m,n$ - in my case calculated by Excel solver) but I need the rest of the combination of coefficients that results in the function value ($100$).

Can I calculate that somehow?

  • 1
    $\begingroup$ Are your variables continuous or integer ? $\endgroup$
    – Kuifje
    Feb 12, 2020 at 8:43
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    $\begingroup$ Hi and welcome. Before I answer, did you google "enumerate all optimal solutions" and found links like this one? $\endgroup$ Feb 12, 2020 at 9:08
  • 1
    $\begingroup$ To add @Marco Lübbecke mentioned, if you are interested to enumerate all (optimal) feasible solutions, you would like to see this by SCIP or this in OR.SE. $\endgroup$
    – A.Omidi
    Feb 12, 2020 at 9:44
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    $\begingroup$ You mentioned the solution being the lower case letters but also said "the rest of the combination[s] of coefficients". Are the lower case letters coefficients and the upper case letters variables, or vice versa? $\endgroup$
    – prubin
    Feb 12, 2020 at 20:44


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