In linear programing can both maximisation and minimization be the objective function of a problem?

Answer 1

I am pretty sure that the answer is "yes", though quite often, what is desired is a maximization (for example, to maximize profits). Since any minimization function can easily be converted into a maximization function, I see no reason why it shouldn't be possible to minimize a problem.For example, "minimizing the loss" can be converted to "maximizing profits". More generally, if the function you want to minimize is f(x), just define a new function, which we might call g(x), defined as g(x) = -f(x). Thus, minimizing f(x) is equivalent to maximizing g(x).

Answer 2

Not at the same time.