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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.

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