Formulate a linear programming problem that can be used to solve the following question. An airline has three types of airplanes and has contracted with a tour group to provide transportation for a minimum of 78 first-class, 62 tourist, and 110 economy-class passengers. The first plane costs $4100 for the trip and can accommodate 48 first-class, 14 tourist, and 30 economy-class passengers; the second plane costs $4900 for the trip and can accommodate 16 first-class, 8 tourist, and 42 economy-class passengers; the third plane costs $6100 for the trip and can accommodate 20 first-class, 32 tourist, and 14 economy-class passengers. How many of each type of airplane should be used to minimize the operating cost