Most online shops have a half-yard or higher minimum cut. The reason is that it takes just as much time, i.e. labor cost, to cut a quarter-yard or less as it does a half-yard, and the labor involved in pulling, cutting, folding and putting away for a very small cut is more than the profit involved in that cut.
Our minimum cut on regular priced fabrics is 1/2 yard. Currently we're selling in 1/2 yard increments, but we've gotten our cart software modified so that soon we'll be selling in smaller increments -- but we'll still keep the 1/2 yard minimum cut because of the labor issue.