$3(1\mathrm{.}5$ points$)$ A joint mode$-$destination vehicle$-$based social$/$recreational trip logit model is estimated with the following coefficients:

Variable

Auto constant

Travel time in minutes

Population in thousands

Amusement floor space $($in thousands of $ft2)$

$\backslash$table$[[$Auto coefficient,Bus coe$],[0\mathrm{.}9,0\mathrm{.}0],[-0\mathrm{.}22,-0\mathrm{.}22],[0\mathrm{.}16,0\mathrm{.}16],[0\mathrm{.}11,0\mathrm{.}11]]$

It is known that $500$ social$/$recreational trips will depart from a residential area during the peak hour. There are three possible trip destinations with the following characteristics:

$\backslash$table$[[,$Travel time $($in minutes$),,],[,$Auto,Bus,Population $($in thousands$),$Amusement floor space $($in thousands of $ft2)],[$Destination $1,14,17,12\mathrm{.}4,13\mathrm{.}0],[$Destination $2,5,8,8\mathrm{.}2,9\mathrm{.}2],[$Destination $3,18,24,5\mathrm{.}8,21\mathrm{.}0]]$

Determine the distribution of trips by mode and destination