That is one way to give a clear answer. I’m not ruling out there being any other ways but I don’t have one to suggest.
Why x+y is a bad answer is one of the main topics of Multi-Factor Decision Making Math. The essay also applies to x*y some.
My answer is that maximizing 2+ (qualitatively) different things is undefined or impossible in general.
If you have an answer that individually maximizes every single one of the things, then that works. But in general that isn’t available.
Notable previous comments:
The implicit premise here is that you can only maximize a single value, not pairs, which is correct.
But there is no standard, default or common sense way to convert pairs to single quantities in general. This is the problem of combining different dimensions, like length and time, or width and temperature, which can only be done contextually or in special cases (and often only approximately), not universally or generically.
This is correct. You can just say none of the options maximize every individual factor, so none are the combined maximum. That’s a simple way to think of it.
Relating this back to the article and your comments, when Friedman says to maximize profit, it doesn’t mean to maximize profit and customer satisfaction and supplier retention and employee productivity. If you want all four of those things, you make them all goals or high priorities or something; that isn’t maximization.
Friedman means to maximize profit only. Maximizing means just maximizing one thing. He means don’t maximize customer satisfaction.
While you can’t maximize two things, you can maximize one thing while obeying any number of constraints. Any option that violates even one constraint is simply rejected, and the highest scoring option that follows every constraint is the maximum. Friedman says to follow the law while maximizing profit, so that’s constrained maximization.
Make sense? @Eternity too. If so, the next thing to consider may be revisiting Multi-Factor Decision Making Math to evaluate what you didn’t understand previously, and if/why you thought you did understand that, and post mortem what’s going on there. Then continue with the Friedman article.