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.
To find the optimum number of bus rides and taxi rides for a hundred trips, we need to maximize utility while minimizing travel costs.
Given the utility function U(b, t) = min(b, t), where b represents the bus fare and t represents the taxi fare, and the constraint that b = 3t for the same distance, we can solve the problem as follows:
1. Find the relationship between the bus fare (b) and the taxi fare (t) using the constraint: b = 3t.
2. Substitute this relationship into the utility function: U(3t, t) = min(3t, t).
3. Simplify the utility function: U(t) = min(3t, t). Since the minimum function returns the smaller value, U(t) will be equal to t.
4. We want to minimize travel costs. Since the taxi fare is smaller than the bus fare (t < 3t), we can conclude that taking a taxi will result in lower travel costs.
5. Therefore, for each trip, the consumer should take a taxi ride.
6. For a hundred trips, the optimum number of bus rides and taxi rides will be 0 bus rides and 100 taxi rides.
In summary, the consumer should take a taxi for all 100 trips to minimize travel costs and maximize utility.