Part II: Mode Choice $(25$ pt$)$

Between a residential area and an industrial complex, $5000$ workers $($generating vehicle$-$based trips$)$ depart for work during the peak hour. For all workers, the cost of driving an automobile is $$8\mathrm{.}00$ with a travel time of $30$ minutes, and the bus fare is $$1\mathrm{.}00$ with a travel time of $50$ minutes. Shared$-$ride option always consists of two travelers sharing costs equally.

The utility functions for driving along $($DL$),$ share$-$ride $($SR$)$ and taking bus $($B$)$ are below:

$U_{DL}=2\mathrm{.}0-0\mathrm{.}02(cos{t}_{DL})-0\mathrm{.}3(tim{e}_{DL})$

$U_{SR}=1\mathrm{.}5-0\mathrm{.}02(costsR)-0\mathrm{.}3(R)$

$U_B=1\mathrm{.}2-0\mathrm{.}02(cos{t}_B)-0\mathrm{.}2(tim{e}_B)$

where $U_{DL},U_{SR}$ and $U_B$ refer to the utility of DL$,$ SR and B$,$ respectively; cost $DL,$ costsp and $cos{t}_B$ refer to the cost of DL$,$ SR and B$,$ respectively; and timeDL, timesR and time $B$ refer to the travel time of $DL,SR$ and $B,$ respectively.

Answer the following questigns.

What is the percentage of thorkers who will drive along to work $,$ and howmany workers are expected to take bus to wgltars? $(1{}^{pt})$ Note: Please nighlight your atrontagl?

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