Southwest should be one of the carriers.
Unfortunatly I don't know.
The airlines that fly from JFK to Midway in Chicago are Delta and Sun Country. Neither offer nonstop flights for this route at this time. Nonstop flights are available for JFK to Chicago ORD on American, Delta, and JetBlue.
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US Airways offers nonstop air service from Chicago O'Hare to Sarasota/Bradenton airport.
Northwest Airlines Flight 1500 / 285 10:18am Chicago, IL (MDW) 4:22pm Memphis, TN (MEM) 6hrs 4min - Change planes in Detroit, MI (DTW) $518 per person Delta Airlines, AirTran Airways, Continental Airlines
no it does not fly it use to back in 2006 same as american airlines
Southwest Airlines operates direct flights between Tampa International Airport (IATA: TPA, ICAO: KTPA) and Chicago Midway International Airport (IATA: MDW, ICAO: KMDW)
ATA/Air Tran/ Comair/Delta/Southwest/ Frontier/Continental
Dallas Love Field in Dallas, Texas.
A direct, midweek economy flight on Southwest Airlines in early March flying from Chicago Midway (MDW) to Dallas Love Field (DAL) from $250, return ($119 one way). Continental fly from Chicago O'Hare (ORD) with a change at Houston from about $300, return.
America, United, Delta and Southwest all fly between these airports. Southwest flies into Chicag Midway rather than Chicago O'Hare.
Southwest Airlines uses turnaround operations to avoid delays at busy hubs. The airports used as turnaround airports are Chicago-Midway, Baltimore-Washington, Las Vegas, Denver, Phoenix, Houston (Hobby), Atlanta, Orlando, Dallas (Love Field), Los Angeles (LAX).