$($a$)$ Destination choice

Assume there are $2000$ households in the new residential area. CFTA would like to estimate the destination choice of the new residents on Saturday evening peak hour $(6pm7pm).$ There are only three possible destinations $($unfortunately$)$: $1)$ movie theater, $2)$ restaurant, $3)$ stay at home. Based on survey results, CFTA knows that:

All the household members will travel together on Saturday evening

All the trips are car$-$based

The destination choice follows the Logit model

The deterministic utility function depends on four factors: constant, travel time, cost, and happiness. The coefficients of each factor are as follows:

$\backslash$table$[[$Variable$,$Coeff.$],[$Constant$,0],[$Travel Time $(min),-0\mathrm{.}2],[$Cost $($$$),-0\mathrm{.}3],[$Happiness$,2]]$

Characteristics of each activity are as follows:

$\backslash$table$[[$Variable$,$Movie Theater,Restaurant,Stay at home$],[$Travel Time $(min),20,10,0],[$Cost $($$$),8,20,0],[$Happiness $($scale $0$ to $5),3,4,0]]$

Using the Logit model, determine how many trips from this new housing area will go to each recreational option.