V bus [Problem 2] Consider a three-mode choice situation in which a worker must choose between auto, bus, and walking for the journey to work. The systematic utility functions associated with these alternatives might take the form: Vauto = 1.0 -0.1 (TTauto) - 0.05 (TCauto) -0.1 (TThus) - 0.05 (TChus) Vwalk = -0.5 -0.1 (TT walk) Where TT = travel time by mode i, minutes TC = travel cost by mode i, dollars Assume that a given individual is faced with travel times of 5, 15, and 20 minutes for the auto, bus, and walk modes, respectively. Similarly, out-of-pocket travel costs by auto and bus are $1.60 and $1.50, respectively. In this case, the values of the systemati utility functions are: Vauto = 0.42 Vous = -1.575 Vwalk = -2.5 From the multinomial logit model given by . the probabilities of this worker choosing the auto, bus and work modes are 84.1%, 11.4% and 4.5%, respectively. The buses in the above example are operated by the Red Bus Transit Co. Assume that a new operator, Blue Coach Lines, introduces a service that is identical to that of the Red Bus Transit Co. (i.e., 15-minute travel time, $1.50 fares), except that the service is provided blue buses rather than red. We now have four "modes" in the choice set: auto, red bus, blue bus, and walk. Compare the probabilities of each of four modes being chosen using equation below (and assuming that the blue bus utility function is the same as the red bus function). Compare these probabilities with those for the three-mode example. Are these results reasonable, especially given that the model ignores frequency of service? Why or why not? Vit Pit = gjeve