$10,000$ trips will be made from Zone $1$ to Zone $2.$ Three travel modes, auto, rail and bus, are available to travelers. If the auto mode is used, the travel time will be $30$ minutes and the travel cost will be $$3\mathrm{.}00.$ If the rail mode is used, the travel time will be $45$ minutes and the rail ticket will cost $$2\mathrm{.}00.$ If the bus mode is used, the travel time will be $60$ minutes and the bus ticket will cost $$1\mathrm{.}00.$ Transportation planners have estimated utility functions for these three modes as:

In those utility functions, travel time is measured in minutes and travel cost is measured in dollars. Apply the Multinomial Logit model to calculate the number of trips using auto, rail and walk.