=Along each leg of this route, there is a minimum and a maximum amount of fuel that may be carried. This and additional information is provided in the table above.

The regular fuel consumption is based on the plane carrying the minimum amount of fuel. If more than this is carried, the amount of fuel consumed is higher. Specifically, for each 1,000 gallons of fuel above the minimum, 5% (or 50 gallons per 1,000 gallons of extra fuel) is lost due to excess fuel consumption. For example, if 25,000 gallons of fuel were on board when the plane takes off from Atlanta, the fuel consumed on this route would be 12 + 0.05 = 12.05 thousand gallons. If 26 thousand gallons were on board, the fuel consumed would be increased by another 0.05 thousand, for a total of 12.1 thousand gallons.

Formulate this as an LP problem to minimize the cost. How many gallons should be purchased in each city? What is the total cost of this?