Dollar General Corp. has raised its takeover offer for Family Dollar Stores Inc. to $9.1 billion, and also warned that it may appeal directly to shareholders if the new offer is rebuffed. Dollar General said it is willing to pay a break up fee of $500 million if the acquisition violated competition laws; which according to Family Dollar was the main reason Dollar General’s first offer of $8.95 billion was rebuffed. Family Dollar has opted for an $8.5 billion cash and stock bid from Dollar Tree Inc., but also said the board would review the new offer from Dollar General.