Ex $5.$ A logit model has a utility factor function of the form: $(15$ pts$)$

$U=-0\mathrm{.}0754A-0\mathrm{.}5W-0\mathrm{.}04R-0\mathrm{.}02C$

where,

A $=$ access time in minutes

$W=$ Waiting time in minutes

$R=$ Riding time in minutes

$C=$ Out$-$of$-$pocket costs in cents

a$)$ What are the modal split estimates $($probabilities$)$ for the following data:

$\backslash$table$[[$Mode$,$A$,$W$,$R$,$C$],[$Auto$,6,1,25,300],[$Rail$,7,10,15,75],[$Bus$,10,15,35,60],[$Bike$,1,0,45,10]]$