6. (10 points) According to a travel survey in the Tuscaloosa Alabama region, the following two utility functions explain travelers' choices between car and bus. V_{\text {car }}=-0.005-0.01 \text {

OPTC }-0.08 \text { WALK - } 0.06 \text { WAIT }=0.04 \text { IVTT } \mathrm{V}_{\text {bus }}=-0.008-0.01 \text { OPTC }-0.08 \text { WALK }-0.06 \text { WAIT }-0.02 \text { IVT } where, OPTC is out-of-pocket travel cost; WALK is the walking time; WAIT is the waiting time; and IVTT is the in-vehicle travel time. a) Apply the logit model to calculate the probabilities of driving a car and taking a bus if the values of the independent variables (trip characteristics) are: b) If shared autonomous vehicles (SAVS) are introduced to the public in the City of Tuscaloosa, what is probability of choosing SAVs over other modes (car and bus)?Assume the OPTC for car and bus is still 100 and 300 respectively. The utility function for the mode of SAVS is \mathrm{V}_{\mathrm{SAV}}=-0.008-0.01 \text { OPTC }-0.08 \text { WALK }-0.06 \mathrm{WAIT}-0.02 \mathrm{IVTT} And the trips by SAVS have the following attributes: