As per the GTFM, when personal and business travel is combined, comparable quotes should be obtained prior to the travel and the employee will be reimbursed for the lowest available fare. Getting the quotes after the fact is often not possible or will not necessarily meet the travel conditions before the trip.
For example: An employee goes for a two-day conference but stays in the same city for a longer duration for personal travel. If the cost of the entire trip is lower than the cost of travel for the two-day conference alone, then the employee will be reimbursed the lower of the two amounts. The employee should obtain the quotes for both business plus personal travel and business travel alone prior to the trip.