The utility function of a consumer
U(b,t)=Min(b,t) for where b=busfare and t=taxifare, b=3t for the same distance.For hundred times travel what will be the optimum number of busride and taxiride.
If I understand your notation, bus fare costs 3 times a taxi fare. To maximize utility, your consumer need only minimize travel costs. Ergo, easy, only take a taxi.