OP, you're both overthinking and underthinking the issue. Overthinking, because trying to write out linear algebra equations to solve for whether or not to check luggage borders on the absurd. Yet simultaneously underthinking the issue, because if-- as a fun thought experiment (for certain values of "fun")-- one were to model the situation mathematically the model would need to include significantly more nontrivial factors.
Making it tougher yet is that time is only one of several dimensions that must be considered. Some variables are expressed in currency cost, some in physical effort, some in hassle or aggravation factor, some in loss of functional capability, some in impaired style, some in loss of alternatives in case of plans being scrambled, etc. Many of these dimensions are subjective and difficult to equate to one another. Attempting to craft a definitive mathematical model is a fool's errand.