Given this distribution of cars, find a schedule for minimizing the total distance traveled during the overnight redistribution of the cars.

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The American Rent-a-Car Company has eight outlets in a metropolitan area. American operates under a policy that calls for a specific “target” percentage of all available cars to be located at each outlet at the start of each day. These percentages are summarized in the following table. For example, if 50 cars are available, 10 should be at outlet 1 at the start of the day. At the end of a day, if the current distribution of cars does not comply with the targets, American employees drive the cars overnight from outlet to outlet so that the new distribution meets the specified targets. The distance between each pair of outlets is given in the following table. At the end of a particular day, American finds that the 100 cars currently available are distributed at the outlets as follows. (a) Given this distribution of cars, find a schedule for minimizing the total distance traveled during the overnight redistribution of the cars.

 

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