Mr. Rishab Bajaj, an entrepreneur in New York City, places a bet with some friends that he can travel around the world in 8 days by spending not more than $8000. His friends give him a list of 10 cities which he should pass through on this journey around the world. The fares and times by different modes of transport from each city to the next are given in the table below. Assume that Mr. Bajaj will spend 3 hours in every city if he has to change the mode of transport and 2 hours if he has to continue with the same mode of transport. Mr. Bajaj realizes that he will also have to spend on food and other expenses throughout the journey. Therefore, he will have only $7500 to pay for the travel fares.
What is the minimum total time in which Bajaj can complete his journey within the given budget?
We have already seen in the explanation for previous question, a sequence of routes which takes 171 hours and costs $7225. To get a sequence which takes lesser time, we must look for alternative modes of transport which are faster but not much more expensive. We cannot replace any of the non-air routes by air routes, as that would overshoot the budget. Thus, the only possibility is changing the mode of transport from London to Istanbul from road to rail.
However, if Bajaj travels by rail on all three routes, that would cost $305 more. So he travels by rail on only two routes (Paris to Vienna to Istanbul) and by road from London to Paris. For all other routes, he travels by air, except San Francisco to New York City where he travels by rail.
This sequence would take 151 hours and cost $7490.