With those who feel that the use of an ordinary word for an ordinary notion does not do justice to their vocabulary or sufficiently exhibit their cultivation, feasible is now a prime favorite. Its proper sense is “capable of being done, accomplished, or carried out.” That is, it means the same as “possible” in one of the latter’s sense, and its true function is to be used instead of “possible” where that might be ambiguous. A thunderstorm is possible (but not “feasible”). Irrigation is possible (or, indifferently, “feasible”). A counter-revolution is possible: that is, (a) one may for all we know happen, or (b) we can if we choose bring one about; but, if (b) is the meaning, “feasible” is better than “possible” because it cannot properly bear sense (a) and therefore obviates ambiguity.

The wrong use of “feasible” is that in which… it is allowed to have also the other sense of “possible,” and that of “probable.” This is described by the OED as “hardly a justifable sense etymologically, and… recognized by no dictionary.” It is however becoming very common…

—H W Fowler
Modern English Usage