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1.G. D. White and K. Smith , “The Rental Car Problem,” Coll. Math. J. 27 (5), 374-378 (Nov. 1996). If only one stop is allowed en route, this is a typical optimization problem involving the derivative (spoiler alert—answers given below); If multiple fuel stops are allowed, it can be framed as a multi-variate optimization. If no limit is placed on the number of fuel stops, the optimal solution can be obtained by driving straight to the midpoint and then fueling up continuously (!) to the endpoint, naturally invoking the integral. Answer to single stop version: two-thirds of the way to the final destination.
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