Out luggage was placed on an Allegiant Air flight Friday April 15, 2016. When we arrived at the gate, some 35 minutes before the flight was to take off, we were advised the flight was full and doors closed and we could not get on. Our seats that we paid extra for were sold to another passenger. To make matters worse noone from the airlines can tell us where our bags are and this is 6 days later. They did offer to book us on a flight 7 hours away from our destination for $150.00 which we declined. I have no resolution with this company and I have contacted to TSA to try and get somewhere with them.