Problem $4$: A simple mode choice model has been estimated for work trips in a small urban area to determine the probabilities of travelers selecting various modes. Mode choices are Drive alone $($DL$),$ automobile shared ride $($SR$),$ Bus $($B$)$

The utility functions are:

$U_{DL}=2\mathrm{.}2-0\mathrm{.}2(C_{DL})-0\mathrm{.}03(t{t}_{DL})$

$U_{SR}=0\mathrm{.}8-0\mathrm{.}2(costs{R}_R)-0\mathrm{.}03($ travel timesR $)$

$U_B=-0\mathrm{.}2(C_B)-0\mathrm{.}01(t{t}_B)$

Where $C=$ cost in $ and $tt=$ travel time in minutes

There are $4,000$ travelers in the peak hour departing for work. The shared ride option is always split between two travelers. How many workers take each mode?

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