# All optimal solutions

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?

• Are your variables continuous or integer ? Feb 12, 2020 at 8:43
• Hi and welcome. Before I answer, did you google "enumerate all optimal solutions" and found links like this one? Feb 12, 2020 at 9:08
• 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. Feb 12, 2020 at 9:44
• 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?
– prubin
Feb 12, 2020 at 20:44