Question $5[27$ marks$]$

There are two travel modes from TAZi to TAZj : self$-$drive $(s)$ or rideshare $(r).$ The utility

functions are:

$U_s=-0\mathrm{.}055(T_S)$

$U_r=-0\mathrm{.}030(T_r)-0\mathrm{.}015(C_r)$

where $T_s,T_r$ are the total travel time of the respective mode in minutes and $C_r$ is the cost of

rideshare in dollars. If the total travel times from TAZi to TAZj are $30$ minutes for self$-$drive

and $35$ minutes for rideshare, and the cost of rideshare is $$16,$ compute the utility values for self$-$

drive and rideshare modes followed by the probability of a person taking rideshare.