Suppose you have just purchased a new type of electric car that can only travel 100 miles on a battery. charging during a trip is too slow, so whenever you need more energy, the current battery is taken out and a new one installed by licensed battery-replacement technicians. thus, even if you decide to replace your battery early, you must still pay full price new battery to be installed. moreover, because these batteries are in high demand, no one can afford to own more than one battery at a time.
suppose you are trying to get from san francisco to new york city on the new inter-continental super-highway, which runs in a direct line between these two cities. there are several fueling stations along the way; each station charges a different price for installing a new battery. before you start your trip, you carefully print the wikipedia page listing the locations and prices of every fueling station on the icsh. given this information, how do you decide the best places to stop for new batteries?