Exercise 1 [10 Credits] Use a logit model to determine the probabilities of a group of 5000 work commuters choosing between three modes of travel during the morning peak hour: a) private car, b) bus, c) light rail. The utility functions for the three modes are estimated using the following equations: Uc = 1.6 -0.3C -0.04T Ug = 0.2 - 0.3C -0.04T ULR = 1.2 -0.3C -0.04T where C = cost () and T = travel time (minutes) For all workers: the cost of driving is 3.00 with a travel time of 25 minutes; the bus fare is 0.60 with a travel time of 45 minutes: the rail fare is 1.00 with a travel time of 15 minutes