I originally asked a question here and they suggested that I crosspost it to the OR stack exchange, so that is what I am doing (hopefully correctly?). Here is the question I asked there:
"I know it depends on the specific problem instance, but approximately how large of an MIP problem can we write and still be guaranteed that an optimization solver will find a solution? For instance, if we have a mixed integer program with 1,000 variables and 1,000 constraints, can we be guaranteed that no matter what the variables and constraints are, modern optimization software will be able to spit out a solution in a reasonable time frame (defined as 1 month or less on a standard computer)? What about 1 million variables and constraints, or a billion variables and a million constraints, etc."