They asked me to model their airline problem. An airline operates three aircraft on a daily route that starts at airport A, flies to airport B, then to airport C, and finally returns to airport A. Fuel can be purchased at each airport, with unit fuel prices ​f_A, f_B, f_C. For each flight leg, the aircraft needs a base amount of fuel G. However, carrying additional fuel increases fuel consumption: if the aircraft carries more fuel, it burns extra fuel due to the additional weight. Formulate an optimization model to decide how much fuel to purchase at each airport in order to minimize total fuel purchasing cost, while ensuring that each aircraft has enough fuel to complete every leg of the route.