Excel Solver problem with true/false variables

[abl1]

Hi all,

I'm pretty sure this is a problem Solver can handle somehow, but I can't quite crack the nut. I have a table of ~40 projects (each row is a unique project) with 50 variables (each column is a unique variable). Each project can have some or all of the variables. I have this currently represented as a "1" if a project has one of the variables. I want to select 30 of the 40 projects so that as many of the 50 variables have a score of 10 or higher. However, more than 10 is not helpful.


If that's not clear, a perfect score would be if the the 30 of the 40 projects selected resulted in each variable having a score of 10 or higher (higher than 10 is meaningless though). An optimization model that gets really high scores in a couple of variables is, for my purposes, worse than a model that chooses projects that results in a score at or near 10 for lots of variables. I'd rather sacrifice a project selection outcome that results in a variable having a total of 11 (as opposed to 10) for an outcome where a different variable has a total of 3 (as opposed to say 2), all else being equal.

I'm happy to try and clarify better based on feedback or try something else besides Solver! I've attached my data with dummy project and variable names.

Many thanks.