57 Transeast Airlines flies planes on the following route:

L.A.–Houston–N.Y.–Miami–L.A. The length (in miles) of each segment of this trip is as follows: L.A.–Houston, 1,500 miles; Houston–N.Y., 1,700 miles; N.Y.–Miami, 1,300 miles; Miami–L.A., 2,700 miles. At each stop, the plane may purchase up to 10,000 gallons of fuel. The price of fuel at each city is as follows: L.A., 88¢; Houston, 15¢; N.Y.,

$1.05; Miami, 95¢. The plane’s fuel tank can hold at most 12,000 gallons. To allow for the possibility of circling over a landing site, we require that the ending fuel level for each leg of the flight be at least 600 gallons. The number of gallons used per mile on each leg of the flight is 1 + (average fuel level on leg of flight/2,000)

To simplify matters, assume that the average fuel level on any leg of the flight is

(Fuel level at start of leg) + (fuel level at end of leg)