Exercise: Greydog Bus Company operates buses between Boston and Washington, D$.$C$.$ A bus trip between these two cities takes $6$ hours. Federal Boston to Washington and one from Washington to Boston. Table $54$ gives the departure times for the buses. Greydog's goal is to minimize the total downtime for all drivers. How should Greydog assign crews to trips? Note: It is permissible for a driver's "day" to overlap midnight. For example, a Washington$-$based driver can be assigned to the Washington$-$Boston $3$ P$.$M$.$ trip and the Boston$-$Washington $6$ A$.$M$.$ trip.

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